Номер 2, страница 148 - гдз по физике 11 класс учебник Касьянов

Физика, 11 класс Учебник, автор: Касьянов Валерий Алексеевич, издательство Просвещение, Москва, 2019, белого цвета

Авторы: Касьянов В. А.

Тип: Учебник

Издательство: Просвещение, Дрофа

Год издания: 2019 - 2026

Уровень обучения: базовый

Цвет обложки: белый, красный

ISBN: 978-5-09-099511-5

Глава 5. Волновые свойства света. Параграф 41. Взаимное усиление и ослабление волн в пространстве. Задачи - номер 2, страница 148.

App\Models\Task {#1030 // resources/views/models/task/default.blade.php
  #connection: "mysql"
  #table: "tasks"
  #primaryKey: "id"
  #keyType: "int"
  +incrementing: true
  #with: []
  #withCount: []
  +preventsLazyLoading: false
  #perPage: 15
  +exists: true
  +wasRecentlyCreated: false
  #escapeWhenCastingToString: false
  #attributes: array:24 [
    "id" => 598365
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "148"
    "field_page_end" => null
    "field_url" => "/11-klass/fizika/kasyanov/41-2-2"
    "field_display_title" => "2"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037
      #items: array:1 [
        0 => App\Models\Term {#1036
          #connection: "mysql"
          #table: "terms"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: false
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => ""
          ]
          #original: array:6 [
            "id" => 26
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "name" => "номер"
            "field_cases" => array:6 [
              "field_accusative_case" => "номер"
              "field_creative_case" => "номером"
              "field_dative_case" => "номеру"
              "field_genitive_case" => "номера"
              "field_nominative_case" => "номер"
              "field_prepositional_case" => "номере"
            ]
            "field_short_name" => ""
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
    "field_description_top" => null
    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035
      #items: []
      #escapeWhenCastingToString: false
    }
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046
      #items: array:1 [
        0 => App\Models\Branch {#1045
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 598001
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Волновые свойства света"
            "field_branch_order" => "5"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050
              #items: array:1 [
                0 => App\Models\Term {#1047
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "130"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1083
              #items: array:1 [
                0 => App\Models\Book {#1049
                  #connection: "mysql"
                  #table: "books"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:50 [
                    "id" => 282
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1051
                      #items: array:1 [
                        0 => App\Models\Term {#1048
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #original: array:10 [
                            "id" => 6493
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Физика"
                            "field_abbreviated_name" => null
                            "field_cases" => array:6 [ …6]
                            "field_foreign_lang_name" => null
                            "field_short_name" => null
                            "field_subject_type" => "technical_subject"
                            "field_translit" => "fizika"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1052
                      #items: array:1 [
                        0 => App\Models\Term {#1053
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5460
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "11"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "odinadcatyj"
                          ]
                          #original: array:6 [
                            "id" => 5460
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "11"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "odinadcatyj"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054
                      #items: array:2 [
                        0 => App\Models\Term {#1055
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #original: array:6 [
                            "id" => 5153
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Просвещение"
                            "field_cases" => null
                            "field_translit" => "prosveschenie"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1056
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 5148
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дрофа"
                            "field_cases" => null
                            "field_translit" => "drofa"
                          ]
                          #original: array:6 [
                            "id" => 5148
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Дрофа"
                            "field_cases" => null
                            "field_translit" => "drofa"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1057
                      #items: array:1 [
                        0 => App\Models\Term {#1058
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:12 [
                            "id" => 4566
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Касьянов"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Валерий"
                            "field_patronymic" => "Алексеевич"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4566
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Касьянов"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Валерий"
                            "field_patronymic" => "Алексеевич"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060
                      #items: array:1 [
                        0 => App\Models\Term {#1061
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #original: array:10 [
                            "id" => 6671
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Учебник"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => null
                            "field_short_name" => null
                            "field_short_name_foreign" => null
                            "field_translit" => "uchebnik"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1062
                      #items: array:1 [
                        0 => App\Models\Term {#1063
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1064
                      #items: array:1 [
                        0 => App\Models\Term {#1065
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1066
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1067
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068
                      #items: array:1 [
                        0 => App\Models\Term {#1069
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 38
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "базовый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "bazovyy"
                          ]
                          #original: array:6 [
                            "id" => 38
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "базовый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "bazovyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070
                      #items: array:1 [
                        0 => App\Models\Term {#1071
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #original: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "10"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072
                      #items: array:1 [
                        0 => App\Models\Term {#1073
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #original: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1074
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2019"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "469"
                    "field_priority" => "4"
                    "field_default_folder" => "/fizika_11/kasyanov-u-b-22/"
                    "field_isbn" => "978-5-09-099511-5"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_11/kasyanov-u-b-22/covers/cover1.webp?ts=1738004253"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_11/kasyanov-u-b-22/covers/cover1.webp?ts=1738004253"
                        "alt" => ""
                        "width" => "2277"
                        "height" => "3035"
                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/11-klass/fizika/kasyanov"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078
                      #items: array:2 [
                        0 => App\Models\Term {#1079
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 45
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "белый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "belyy"
                          ]
                          #original: array:6 [
                            "id" => 45
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "белый"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "belyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                        1 => App\Models\Term {#1080
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 46
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "красный"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "krasnyy"
                          ]
                          #original: array:6 [
                            "id" => 46
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "красный"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "krasnyy"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Нюансы предмета с ГДЗ </h2> <p> Физика - очень интересный предмет, который нравится многим школьникам. Но наблюдать за опытами им кажется более увлекательным, чем решать сложные уравнения. Более того, есть ребята, которые так и не научились понимать, каким именно образом нужно выражать те или иные явления при помощи формул. Это весьма затрудняет работу над новым материалом. Благодаря справочнику <strong>ГДЗ по физике 11 класс Учебник Касьянов В.А. (Дрофа, Просвещение)</strong> можно значительно облегчить учебный процесс. </p> <p> Больше всего сложностей у учащихся связано с освоением следующих тем: </p> <ol> <li>Как измеряется сила тока и напряжения?</li> <li>Что такое электрический ток?</li> <li>Действие магнитного поля на движущиеся заряженные частицы.</li> <li>Электромагнитная индукция.</li> <li>Передача электроэнергии на расстояние.</li> </ol> <p> Труднее всего ученикам запомнить немалые объемы информации, что из чего проистекает. Соответственно, это затрудняет и работу над практическими упражнениями. В итоге, даже при большом интересе к непростой науке, у многих подростков наблюдаются проблемы с успеваемостью. Чтобы не испортить себе аттестат плохими оценками и приобрести необходимые навыки, старшеклассникам стоит воспользоваться решебником. </p> <h2> Польза ГДЗ для выпускников </h2> <p> Ребятам приходится много внимания уделять подготовке к экзаменам. Из-за этого они очень мало работают над другими предметами, особенно теми, которые кажутся не такими уж сложными. С первого взгляда физика представляется достаточно простой, ведь со всеми изучаемыми явлениями ребята в той или иной мере уже знакомы. Однако это ошибочное мнение нередко становится причиной появления крупных пробелов. Чтобы их избежать, стоит воспользоваться <strong>решебником Касьянова по физике за 11 класс</strong>. </p> <p> Систематически применяя онлайн-издание, ученики смогут: </p> <ol> <li>приобрести качественные знания, которые пригодятся в будущем;</li> <li>восполнить все имеющиеся упущения;</li> <li>улучшить оценки за домашние задания и работу на уроках;</li> <li>тщательно, но быстро прорабатывать допущенные ошибки.</li> </ol> <p> В решебнике значительно упрощена подача материала, так что сильно отставшие от программы ученики без особого труда справятся со всеми поставленными перед ними требованиями. Каждый пользователь получит возможность добиться отличных результатов, если внимательно изучит представленные в справочнике сведения. </p> <h2> Особенности строения решебника </h2> <p> Современные учебные пособия больше рассчитаны на закрепление уже полученных навыков, поэтому теория как таковая содержится в них в весьма сжатом виде. Школьникам часто приходится искать дополнительную информацию, чтобы понять, о чем идет речь в параграфах. Это отнимает много времени, которого у ребят по сути нет. Издание <strong>ГДЗ «Физика 11 класс Учебник Касьянов В.А.»</strong> упростит работу над дисциплиной и позволит лучше усвоить текущую программу. </p> <p> Представленная в электронном пособии информация оказывает такое влияние по нескольким причинам: </p> <ul> <li>она составлена опытными методистами;</li> <li>соответствует оригинальному учебнику и дополняет его;</li> <li>не имеет похожих аналогов;</li> <li>отвечает требованиям ФГОС.</li> </ul> <p> Для полноценного восприятия программы не стоит просто списывать из решебника, так как это не привьет понимания многочисленных деталей. Ученикам не стоит забывать о том, что работа со сборником призвана не заменить освоение теории, а разъяснить сложные моменты. Поэтому использовать справочник нужно для самоконтроля, а не как шпаргалку. </p>"
                    "breadcrumbs" => array:3 [
                      "class" => 382
                      "subject" => 556
                      "class_subject" => 495
                    ]
                  ]
                  #original: array:50 [
                    "id" => 282
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_tree_default_status" => "tasks"
                    "field_pages_status" => null
                    "field_subject" => Illuminate\Database\Eloquent\Collection {#1051}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1052}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1057}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1059}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1060}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1062}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1064}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1066}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1067}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1068}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1070}
                    "field_publication_number" => "10"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1072}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1074}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2019"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "469"
                    "field_priority" => "4"
                    "field_default_folder" => "/fizika_11/kasyanov-u-b-22/"
                    "field_isbn" => "978-5-09-099511-5"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_11/kasyanov-u-b-22/covers/cover1.webp?ts=1738004253"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_11/kasyanov-u-b-22/covers/cover1.webp?ts=1738004253"
                        "alt" => ""
                        "width" => "2277"
                        "height" => "3035"
                      ]
                    ]
                    "field_popular_book" => null
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1075}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1076}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1077}
                    "field_url" => "/11-klass/fizika/kasyanov"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1078}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => "<!--Текст в низу страницы--> <h2> Нюансы предмета с ГДЗ </h2> <p> Физика - очень интересный предмет, который нравится многим школьникам. Но наблюдать за опытами им кажется более увлекательным, чем решать сложные уравнения. Более того, есть ребята, которые так и не научились понимать, каким именно образом нужно выражать те или иные явления при помощи формул. Это весьма затрудняет работу над новым материалом. Благодаря справочнику <strong>ГДЗ по физике 11 класс Учебник Касьянов В.А. (Дрофа, Просвещение)</strong> можно значительно облегчить учебный процесс. </p> <p> Больше всего сложностей у учащихся связано с освоением следующих тем: </p> <ol> <li>Как измеряется сила тока и напряжения?</li> <li>Что такое электрический ток?</li> <li>Действие магнитного поля на движущиеся заряженные частицы.</li> <li>Электромагнитная индукция.</li> <li>Передача электроэнергии на расстояние.</li> </ol> <p> Труднее всего ученикам запомнить немалые объемы информации, что из чего проистекает. Соответственно, это затрудняет и работу над практическими упражнениями. В итоге, даже при большом интересе к непростой науке, у многих подростков наблюдаются проблемы с успеваемостью. Чтобы не испортить себе аттестат плохими оценками и приобрести необходимые навыки, старшеклассникам стоит воспользоваться решебником. </p> <h2> Польза ГДЗ для выпускников </h2> <p> Ребятам приходится много внимания уделять подготовке к экзаменам. Из-за этого они очень мало работают над другими предметами, особенно теми, которые кажутся не такими уж сложными. С первого взгляда физика представляется достаточно простой, ведь со всеми изучаемыми явлениями ребята в той или иной мере уже знакомы. Однако это ошибочное мнение нередко становится причиной появления крупных пробелов. Чтобы их избежать, стоит воспользоваться <strong>решебником Касьянова по физике за 11 класс</strong>. </p> <p> Систематически применяя онлайн-издание, ученики смогут: </p> <ol> <li>приобрести качественные знания, которые пригодятся в будущем;</li> <li>восполнить все имеющиеся упущения;</li> <li>улучшить оценки за домашние задания и работу на уроках;</li> <li>тщательно, но быстро прорабатывать допущенные ошибки.</li> </ol> <p> В решебнике значительно упрощена подача материала, так что сильно отставшие от программы ученики без особого труда справятся со всеми поставленными перед ними требованиями. Каждый пользователь получит возможность добиться отличных результатов, если внимательно изучит представленные в справочнике сведения. </p> <h2> Особенности строения решебника </h2> <p> Современные учебные пособия больше рассчитаны на закрепление уже полученных навыков, поэтому теория как таковая содержится в них в весьма сжатом виде. Школьникам часто приходится искать дополнительную информацию, чтобы понять, о чем идет речь в параграфах. Это отнимает много времени, которого у ребят по сути нет. Издание <strong>ГДЗ «Физика 11 класс Учебник Касьянов В.А.»</strong> упростит работу над дисциплиной и позволит лучше усвоить текущую программу. </p> <p> Представленная в электронном пособии информация оказывает такое влияние по нескольким причинам: </p> <ul> <li>она составлена опытными методистами;</li> <li>соответствует оригинальному учебнику и дополняет его;</li> <li>не имеет похожих аналогов;</li> <li>отвечает требованиям ФГОС.</li> </ul> <p> Для полноценного восприятия программы не стоит просто списывать из решебника, так как это не привьет понимания многочисленных деталей. Ученикам не стоит забывать о том, что работа со сборником призвана не заменить освоение теории, а разъяснить сложные моменты. Поэтому использовать справочник нужно для самоконтроля, а не как шпаргалку. </p>"
                    "breadcrumbs" => array:3 [
                      "class" => 382
                      "subject" => 556
                      "class_subject" => 495
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598001
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Волновые свойства света"
            "field_branch_order" => "5"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050}
            "field_page_start" => "130"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1083}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1114
      #items: array:3 [
        0 => App\Models\Branch {#1124
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 598001
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Волновые свойства света"
            "field_branch_order" => "5"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125
              #items: array:1 [
                0 => App\Models\Term {#1047}
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "130"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1126
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598001
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Волновые свойства света"
            "field_branch_order" => "5"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125}
            "field_page_start" => "130"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1126}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1128
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 598012
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Взаимное усиление и ослабление волн в пространстве"
            "field_branch_order" => "41"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132
              #items: array:1 [
                0 => App\Models\Term {#1129
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #original: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "144"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1131
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130
              #items: array:1 [
                0 => App\Models\Branch {#1045}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598012
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Взаимное усиление и ослабление волн в пространстве"
            "field_branch_order" => "41"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132}
            "field_page_start" => "144"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1131}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1133
          #connection: "mysql"
          #table: "branches"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:24 [
            "id" => 598014
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Задачи"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "148"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1135
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144
              #items: array:1 [
                0 => App\Models\Branch {#1143
                  #connection: "mysql"
                  #table: "branches"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598012
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Взаимное усиление и ослабление волн в пространстве"
                    "field_branch_order" => "41"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 …2}
                    "field_page_start" => "144"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1146 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 …2}
                  ]
                  #original: array:24 [
                    "id" => 598012
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Взаимное усиление и ослабление волн в пространстве"
                    "field_branch_order" => "41"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1145 …2}
                    "field_page_start" => "144"
                    "field_branch_display" => "0"
                    "field_branch_expanded" => "0"
                    "field_display_branch_in_title" => "1"
                    "field_display_task_interval" => "0"
                    "field_display_branch_page" => "1"
                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1146 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1147 …2}
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 598014
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Задачи"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1134}
            "field_page_start" => "148"
            "field_branch_display" => "0"
            "field_branch_expanded" => "0"
            "field_display_branch_in_title" => "1"
            "field_display_task_interval" => "0"
            "field_display_branch_page" => "1"
            "field_branch_title_in_content" => "0"
            "field_navigation_title" => null
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "field_branch_cover" => []
            "field_branch_covers" => []
            "book" => Illuminate\Database\Eloquent\Collection {#1135}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1144}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1112
      #items: array:3 [
        0 => App\Models\Element {#1098
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:7 [
            "id" => 757975
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1089
              #items: array:1 [
                0 => App\Models\Edition {#1097
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 1660
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "pasha"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1094 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 1660
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1093 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "pasha"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1094 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "text" => "<p><strong>2.</strong> Разность хода между лучами от двух когерентных источников в воздухе 6 мкм. Какой станет разность хода между ними в воде ($n = 4/3$)?</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "2-1.jpg"
                "alt" => null
                "width" => "957"
                "height" => 102
                "path" => "/media/fizika_11/kasyanov-u-b-22/0-41-2/2-1.webp?ts=1738130800"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 757975
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1089}
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "text" => "<p><strong>2.</strong> Разность хода между лучами от двух когерентных источников в воздухе 6 мкм. Какой станет разность хода между ними в воде ($n = 4/3$)?</p>"
            "img" => array:1 [
              0 => array:5 [
                "name" => "2-1.jpg"
                "alt" => null
                "width" => "957"
                "height" => 102
                "path" => "/media/fizika_11/kasyanov-u-b-22/0-41-2/2-1.webp?ts=1738130800"
              ]
            ]
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1105
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 757916
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1095
              #items: array:1 [
                0 => App\Models\Edition {#1103
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 1661
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "image"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Неизвестный"
                    "field_moderator" => "anna"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1102 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2}
                    "field_process_formula" => ""
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 1661
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "image"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Неизвестный"
                    "field_moderator" => "anna"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1102 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099 …2}
                    "field_process_formula" => ""
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "2-1.jpg"
                "alt" => null
                "width" => "700"
                "height" => 1578
                "path" => "/media/fizika_11/kasyanov-u-b-22/1-41-2/2-1.webp?ts=1738130793"
              ]
            ]
          ]
          #original: array:6 [
            "id" => 757916
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1095}
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "img" => array:1 [
              0 => array:5 [
                "name" => "2-1.jpg"
                "alt" => null
                "width" => "700"
                "height" => 1578
                "path" => "/media/fizika_11/kasyanov-u-b-22/1-41-2/2-1.webp?ts=1738130793"
              ]
            ]
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Element {#1090
          #connection: "mysql"
          #table: "elements"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:6 [
            "id" => 1477475
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1034
              #items: array:1 [
                0 => App\Models\Edition {#1088
                  #connection: "mysql"
                  #table: "editions"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:21 [
                    "id" => 5427
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение 2"
                    "field_order" => "3"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "2-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 5427
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение 2"
                    "field_order" => "3"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1087 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "2-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1086 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1082 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1084 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "text" => "<p><strong>Дано:</strong></p><p>Оптическая разность хода в воздухе, $\Delta_{возд} = 6$ мкм</p><p>Показатель преломления воды, $n_{воды} = 4/3$</p><p>Показатель преломления воздуха, $n_{возд} \approx 1$</p><blockquote> $\Delta_{возд} = 6 \text{ мкм} = 6 \cdot 10^{-6} \text{ м}$ </blockquote><p><strong>Найти:</strong></p><p>Оптическая разность хода в воде, $\Delta_{воды}$</p><p><strong>Решение:</strong></p><p>Оптическая разность хода $\Delta$ связана с геометрической разностью хода $\delta$ (физическая разница в длинах путей лучей) и показателем преломления среды $n$ по формуле:</p><p>$ \Delta = n \cdot \delta $</p><p>Поскольку геометрическое расположение источников света и точки наблюдения не меняется, геометрическая разность хода $\delta$ остается постоянной при смене среды с воздуха на воду.</p><p>Сначала найдем геометрическую разность хода $\delta$, используя данные для воздуха. Показатель преломления воздуха $n_{возд}$ очень близок к единице, поэтому мы можем принять $n_{возд} = 1$.</p><p>$ \Delta_{возд} = n_{возд} \cdot \delta $</p><p>Отсюда, геометрическая разность хода:</p><p>$ \delta = \frac{\Delta_{возд}}{n_{возд}} = \frac{6 \text{ мкм}}{1} = 6 \text{ мкм} $</p><p>Теперь мы можем рассчитать оптическую разность хода для лучей, распространяющихся в воде, используя показатель преломления воды $n_{воды} = 4/3$.</p><p>$ \Delta_{воды} = n_{воды} \cdot \delta $</p><p>Подставляем известные значения:</p><p>$ \Delta_{воды} = \frac{4}{3} \cdot 6 \text{ мкм} = 4 \cdot \frac{6}{3} \text{ мкм} = 4 \cdot 2 \text{ мкм} = 8 \text{ мкм} $</p><p><strong>Ответ:</strong> разность хода между лучами в воде станет 8 мкм.</p>"
          ]
          #original: array:6 [
            "id" => 1477475
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1034}
            "task" => array:2 [
              "refs" => "598365"
              "type" => "task"
            ]
            "text" => "<p><strong>Дано:</strong></p><p>Оптическая разность хода в воздухе, $\Delta_{возд} = 6$ мкм</p><p>Показатель преломления воды, $n_{воды} = 4/3$</p><p>Показатель преломления воздуха, $n_{возд} \approx 1$</p><blockquote> $\Delta_{возд} = 6 \text{ мкм} = 6 \cdot 10^{-6} \text{ м}$ </blockquote><p><strong>Найти:</strong></p><p>Оптическая разность хода в воде, $\Delta_{воды}$</p><p><strong>Решение:</strong></p><p>Оптическая разность хода $\Delta$ связана с геометрической разностью хода $\delta$ (физическая разница в длинах путей лучей) и показателем преломления среды $n$ по формуле:</p><p>$ \Delta = n \cdot \delta $</p><p>Поскольку геометрическое расположение источников света и точки наблюдения не меняется, геометрическая разность хода $\delta$ остается постоянной при смене среды с воздуха на воду.</p><p>Сначала найдем геометрическую разность хода $\delta$, используя данные для воздуха. Показатель преломления воздуха $n_{возд}$ очень близок к единице, поэтому мы можем принять $n_{возд} = 1$.</p><p>$ \Delta_{возд} = n_{возд} \cdot \delta $</p><p>Отсюда, геометрическая разность хода:</p><p>$ \delta = \frac{\Delta_{возд}}{n_{возд}} = \frac{6 \text{ мкм}}{1} = 6 \text{ мкм} $</p><p>Теперь мы можем рассчитать оптическую разность хода для лучей, распространяющихся в воде, используя показатель преломления воды $n_{воды} = 4/3$.</p><p>$ \Delta_{воды} = n_{воды} \cdot \delta $</p><p>Подставляем известные значения:</p><p>$ \Delta_{воды} = \frac{4}{3} \cdot 6 \text{ мкм} = 4 \cdot \frac{6}{3} \text{ мкм} = 4 \cdot 2 \text{ мкм} = 8 \text{ мкм} $</p><p><strong>Ответ:</strong> разность хода между лучами в воде станет 8 мкм.</p>"
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "next" => array:2 [
      "refs" => "598366"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "598364"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1108
      #items: array:1 [
        0 => App\Models\Book {#1049}
      ]
      #escapeWhenCastingToString: false
    }
    "page" => Illuminate\Database\Eloquent\Collection {#1111
      #items: array:1 [
        0 => App\Models\BookPage {#1042
          #connection: "mysql"
          #table: "book_pages"
          #primaryKey: "id"
          #keyType: "int"
          +incrementing: true
          #with: []
          #withCount: []
          +preventsLazyLoading: false
          #perPage: 15
          +exists: true
          +wasRecentlyCreated: false
          #escapeWhenCastingToString: false
          #attributes: array:21 [
            "id" => 951315
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "148"
            "field_url" => "/11-klass/fizika/kasyanov/page-148"
            "field_display_title" => "148"
            "field_folder" => "1"
            "field_image_name" => "148"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1043
              #items: array:1 [
                0 => App\Models\Book {#1049}
              ]
              #escapeWhenCastingToString: false
            }
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1041
              #items: []
              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1137
              #items: array:1 [
                0 => App\Models\Element {#1117
                  #connection: "mysql"
                  #table: "elements"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:6 [
                    "id" => 1126594
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1136 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #original: array:6 [
                    "id" => 1126594
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1136 …2}
                    "book_page" => array:2 [ …2]
                    "img" => array:1 [ …1]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "next" => array:2 [
              "refs" => "951316"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "951314"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1225
              #items: array:8 [
                0 => App\Models\Task {#1239
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598359
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-1"
                    "field_display_title" => "1"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1240 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1241 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1242 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1323 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1316 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1315 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598359
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-1"
                    "field_display_title" => "1"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1240 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1241 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1242 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1323 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1316 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1315 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                1 => App\Models\Task {#1280
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598360
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-2"
                    "field_display_title" => "2"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1330 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1313 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1314 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1321 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1299 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598360
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-2"
                    "field_display_title" => "2"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1330 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1313 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1314 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1321 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1299 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                2 => App\Models\Task {#1284
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598361
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-3"
                    "field_display_title" => "3"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1304 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1303 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1285 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598361
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-3"
                    "field_display_title" => "3"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1301 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1304 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1303 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1285 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                3 => App\Models\Task {#1302
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598362
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-4"
                    "field_display_title" => "4"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1306 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1288 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1286 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1291 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1275 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598362
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-4"
                    "field_display_title" => "4"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1306 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1288 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1286 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1291 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1275 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                4 => App\Models\Task {#1287
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598363
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-5"
                    "field_display_title" => "5"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1289 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1277 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1247 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1260 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598363
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-1-5"
                    "field_display_title" => "5"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1289 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1277 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1276 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1247 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1260 …2}
                    "page" => array:2 [ …2]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                5 => App\Models\Task {#1278
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [
                    "id" => 598364
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "148"
                    "field_page_end" => null
                    "field_url" => "/11-klass/fizika/kasyanov/41-2-1"
                    "field_display_title" => "1"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 …2}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "field_match" => null
                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1263 …2}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1261 …2}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2}
                    "content" => Illuminate\Database\Eloquent\Collection {#1265 …2}
                    "next" => array:2 [ …2]
                    "previous" => array:2 [ …2]
                    "book" => Illuminate\Database\Eloquent\Collection {#1245 …2}
                    "page" => array:2 [ …2]
                  ]
                  #original: array:24 [
                    "id" => 598364
                     …23
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                6 => App\Models\Task {#1262
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
                7 => App\Models\Task {#1250
                  #connection: "mysql"
                  #table: "tasks"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: true
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:24 [ …24]
                  #original: array:24 [ …24]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [ …1]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:21 [
            "id" => 951315
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "148"
            "field_url" => "/11-klass/fizika/kasyanov/page-148"
            "field_display_title" => "148"
            "field_folder" => "1"
            "field_image_name" => "148"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1040}
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1043}
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
            "field_description_top" => null
            "field_description_bottom" => null
            "edition_groups" => Illuminate\Database\Eloquent\Collection {#1041}
            "content" => Illuminate\Database\Eloquent\Collection {#1137}
            "next" => array:2 [
              "refs" => "951316"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "951314"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1225}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
  ]
  #original: array:24 [
    "id" => 598365
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "148"
    "field_page_end" => null
    "field_url" => "/11-klass/fizika/kasyanov/41-2-2"
    "field_display_title" => "2"
    "field_outside_task" => null
    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037}
    "field_metatags_title" => null
    "field_metatags_description" => null
    "field_h1" => null
    "field_description_top" => null
    "field_description_bottom" => null
    "field_match" => null
    "breadcrumbs" => []
    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035}
    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046}
    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1114}
    "content" => Illuminate\Database\Eloquent\Collection {#1112}
    "next" => array:2 [
      "refs" => "598366"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "598364"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1108}
    "page" => array:2 [
      "refs" => "951315"
      "type" => "book_page"
    ]
  ]
  #changes: []
  #casts: []
  #classCastCache: []
  #attributeCastCache: []
  #dateFormat: null
  #appends: []
  #dispatchesEvents: []
  #observables: []
  #relations: []
  #touches: []
  +timestamps: true
  +usesUniqueIds: false
  #hidden: []
  #visible: []
  #fillable: []
  #guarded: array:1 [
    0 => "*"
  ]
}
№2 (с. 148)
Условие. №2 (с. 148)
скриншот условия
Физика, 11 класс Учебник, автор: Касьянов Валерий Алексеевич, издательство Просвещение, Москва, 2019, белого цвета, страница 148, номер 2, Условие

2. Разность хода между лучами от двух когерентных источников в воздухе 6 мкм. Какой станет разность хода между ними в воде ($n = 4/3$)?

Решение. №2 (с. 148)
Физика, 11 класс Учебник, автор: Касьянов Валерий Алексеевич, издательство Просвещение, Москва, 2019, белого цвета, страница 148, номер 2, Решение
Решение 2. №2 (с. 148)

Дано:

Оптическая разность хода в воздухе, $\Delta_{возд} = 6$ мкм

Показатель преломления воды, $n_{воды} = 4/3$

Показатель преломления воздуха, $n_{возд} \approx 1$

$\Delta_{возд} = 6 \text{ мкм} = 6 \cdot 10^{-6} \text{ м}$

Найти:

Оптическая разность хода в воде, $\Delta_{воды}$

Решение:

Оптическая разность хода $\Delta$ связана с геометрической разностью хода $\delta$ (физическая разница в длинах путей лучей) и показателем преломления среды $n$ по формуле:

$ \Delta = n \cdot \delta $

Поскольку геометрическое расположение источников света и точки наблюдения не меняется, геометрическая разность хода $\delta$ остается постоянной при смене среды с воздуха на воду.

Сначала найдем геометрическую разность хода $\delta$, используя данные для воздуха. Показатель преломления воздуха $n_{возд}$ очень близок к единице, поэтому мы можем принять $n_{возд} = 1$.

$ \Delta_{возд} = n_{возд} \cdot \delta $

Отсюда, геометрическая разность хода:

$ \delta = \frac{\Delta_{возд}}{n_{возд}} = \frac{6 \text{ мкм}}{1} = 6 \text{ мкм} $

Теперь мы можем рассчитать оптическую разность хода для лучей, распространяющихся в воде, используя показатель преломления воды $n_{воды} = 4/3$.

$ \Delta_{воды} = n_{воды} \cdot \delta $

Подставляем известные значения:

$ \Delta_{воды} = \frac{4}{3} \cdot 6 \text{ мкм} = 4 \cdot \frac{6}{3} \text{ мкм} = 4 \cdot 2 \text{ мкм} = 8 \text{ мкм} $

Ответ: разность хода между лучами в воде станет 8 мкм.

Помогло решение? Оставьте отзыв в комментариях ниже.

Присоединяйтесь к Телеграм-группе @top_gdz

Присоединиться

Мы подготовили для вас ответ c подробным объяснением домашего задания по физике за 11 класс, для упражнения номер 2 расположенного на странице 148 к учебнику 2019 года издания для учащихся школ и гимназий.

Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №2 (с. 148), автора: Касьянов (Валерий Алексеевич), ФГОС (старый) базовый уровень обучения учебного пособия издательства Просвещение, Дрофа.