Номер 188, страница 285 - гдз по физике 8 класс учебник Громов, Родина

Задачи и упражнения - номер 188, страница 285.

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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" => 1613055
    "created_at" => "2026-04-10 13:58:26"
    "updated_at" => null
    "field_page_start" => "285"
    "field_page_end" => null
    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-188"
    "field_display_title" => "188"
    "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 {#1076
      #items: array:1 [
        0 => App\Models\Branch {#1034
          #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" => 1612241
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Задачи и упражнения"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "266"
            "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 {#1038
              #items: array:1 [
                0 => App\Models\Book {#1040
                  #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" => 3654
                    "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 {#1041
                      #items: array:1 [
                        0 => App\Models\Term {#1042
                          #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 [ …10]
                          #original: array:10 [ …10]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1043
                      #items: array:1 [
                        0 => App\Models\Term {#1044
                          #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 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045
                      #items: array:1 [
                        0 => App\Models\Term {#1046
                          #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 [ …6]
                          #original: array:6 [ …6]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1047
                      #items: array:5 [
                        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:12 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        1 => App\Models\Term {#1049
                          #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 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        2 => App\Models\Term {#1050
                          #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 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        3 => App\Models\Term {#1051
                          #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 [ …12]
                          #original: array:12 [ …12]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [ …1]
                        }
                        4 => App\Models\Term {#1052
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                           …24
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054
                      #items: array:1 [
                        0 => App\Models\Term {#1055 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1056
                      #items: array:1 [
                        0 => App\Models\Term {#1057 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1058
                      #items: array:1 [
                        0 => App\Models\Term {#1059 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1060
                      #items: array:1 [
                        0 => App\Models\Term {#1061 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1062
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064
                      #items: array:1 [
                        0 => App\Models\Term {#1065 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1066
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067
                      #items: array:1 [
                        0 => App\Models\Term {#1052 …24}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2018"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие для общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "830"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_08/gromov-u/"
                    "field_isbn" => "978-5-09-052825-2"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                        "alt" => ""
                        "width" => "1881"
                        "height" => "2469"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/8-klass/fizika/gromov-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071
                      #items: array:1 [
                        0 => App\Models\Term {#1072 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 379
                      "subject" => 556
                      "class_subject" => 492
                    ]
                  ]
                  #original: array:50 [
                    "id" => 3654
                    "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 {#1041}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1043}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1045}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1047}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1056}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1058}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1060}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1062}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1063}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1064}
                    "field_publication_number" => null
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1066}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2018"
                    "field_publication_year_until" => null
                    "field_part" => ""
                    "field_part_writing" => ""
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное пособие для общеобразовательных организаций"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "830"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_08/gromov-u/"
                    "field_isbn" => "978-5-09-052825-2"
                    "field_cover" => array:1 [
                      0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                    ]
                    "field_cover_alts" => array:1 [
                      0 => ""
                    ]
                    "field_covers" => array:1 [
                      0 => array:4 [
                        "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                        "alt" => ""
                        "width" => "1881"
                        "height" => "2469"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070}
                    "field_url" => "/8-klass/fizika/gromov-uchebnik"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 379
                      "subject" => 556
                      "class_subject" => 492
                    ]
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
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                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1612241
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Задачи и упражнения"
            "field_branch_order" => null
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039}
            "field_page_start" => "266"
            "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 {#1038}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073}
          ]
          #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 {#1074
      #items: array:1 [
        0 => App\Models\Branch {#1034}
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1077
      #items: array:2 [
        0 => App\Models\Element {#1086
          #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" => 1850781
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1095
              #items: array:1 [
                0 => App\Models\Edition {#1087
                  #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" => 6892
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089
                      #items: array:1 [
                        0 => App\Models\Term {#1088 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 6892
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1089}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1090}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1091}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092}
                    "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" => "1613055"
              "type" => "task"
            ]
            "text" => "<p><strong>188.</strong> Постройте изображение, даваемое рассеивающей линзой в случае, показанном на рисунке 29.</p><p>Рис. 29</p>"
            "img" => array:2 [
              0 => array:5 [
                "name" => "188-1.jpg"
                "alt" => null
                "width" => "979"
                "height" => 268
                "path" => "/media/fizika_08/gromov-u/0-upr/188-1.webp?ts=1763478148"
              ]
              1 => array:5 [
                "name" => "188-2.jpg"
                "alt" => null
                "width" => "735"
                "height" => 454
                "path" => "/media/fizika_08/gromov-u/0-upr/188-2.webp?ts=1763478148"
              ]
            ]
          ]
          #original: array:7 [
            "id" => 1850781
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1095}
            "task" => array:2 [
              "refs" => "1613055"
              "type" => "task"
            ]
            "text" => "<p><strong>188.</strong> Постройте изображение, даваемое рассеивающей линзой в случае, показанном на рисунке 29.</p><p>Рис. 29</p>"
            "img" => array:2 [
              0 => array:5 [
                "name" => "188-1.jpg"
                "alt" => null
                "width" => "979"
                "height" => 268
                "path" => "/media/fizika_08/gromov-u/0-upr/188-1.webp?ts=1763478148"
              ]
              1 => array:5 [
                "name" => "188-2.jpg"
                "alt" => null
                "width" => "735"
                "height" => 454
                "path" => "/media/fizika_08/gromov-u/0-upr/188-2.webp?ts=1763478148"
              ]
            ]
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Element {#1093
          #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" => 1900842
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1103
              #items: array:1 [
                0 => App\Models\Edition {#1094
                  #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" => 7854
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097
                      #items: array:1 [
                        0 => App\Models\Term {#1096 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 7854
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Решение"
                    "field_order" => "2"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1097}
                    "field_content_type" => "free"
                    "field_content_mode" => "text"
                    "field_page_content_mode" => ""
                    "field_content_text_checked" => "0"
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Gemini 2.5 Pro"
                    "field_moderator" => "tolik"
                    "field_edition_type" => "solution"
                    "field_root_dir" => "1-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1098}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1099}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100}
                    "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" => "1613055"
              "type" => "task"
            ]
            "text" => "<p><strong>Решение</strong></p><p>Для построения изображения предмета (стрелки) в рассеивающей линзе необходимо построить изображение его верхней точки (острия). Изображение нижней точки, лежащей на главной оптической оси, также будет лежать на оси, под изображением верхней точки.</p><p>Для построения изображения острия стрелки проведем два луча, ход которых известен. Первый луч пустим из острия стрелки параллельно главной оптической оси. После прохождения через рассеивающую линзу он пойдет так, что его продолжение, проведенное в обратную сторону (к предмету), пройдет через мнимый фокус F линзы.</p><p>Второй луч пустим из той же точки (острия стрелки) через оптический центр линзы. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.</p><p>Сами преломленные лучи после линзы являются расходящимися. Чтобы найти изображение, нужно найти точку пересечения их продолжений. Пересечение продолжения первого преломленного луча и второго луча (который не преломился) даст нам положение мнимого изображения острия стрелки. Эта точка будет находиться с той же стороны линзы, что и предмет.</p><p>Опустив перпендикуляр из полученной точки изображения острия на главную оптическую ось, мы найдем изображение основания стрелки. Соединив эти две точки, получим полное изображение предмета.</p><p>Полученное изображение будет мнимым (так как образовано пересечением продолжений лучей), прямым (неперевернутым) и уменьшенным по сравнению с предметом. Оно всегда располагается между линзой и ее мнимым фокусом F.</p><p><strong>Ответ:</strong> Изображение, даваемое рассеивающей линзой, строится с помощью двух лучей, выходящих из верхней точки предмета: луча, параллельного главной оптической оси (после преломления его продолжение проходит через мнимый фокус F), и луча, проходящего через оптический центр линзы (не преломляется). Точка пересечения продолжения первого луча и второго луча дает изображение верхней точки. В результате получается мнимое, прямое, уменьшенное изображение, расположенное между линзой и мнимым фокусом F.</p>"
          ]
          #original: array:6 [
            "id" => 1900842
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1103}
            "task" => array:2 [
              "refs" => "1613055"
              "type" => "task"
            ]
            "text" => "<p><strong>Решение</strong></p><p>Для построения изображения предмета (стрелки) в рассеивающей линзе необходимо построить изображение его верхней точки (острия). Изображение нижней точки, лежащей на главной оптической оси, также будет лежать на оси, под изображением верхней точки.</p><p>Для построения изображения острия стрелки проведем два луча, ход которых известен. Первый луч пустим из острия стрелки параллельно главной оптической оси. После прохождения через рассеивающую линзу он пойдет так, что его продолжение, проведенное в обратную сторону (к предмету), пройдет через мнимый фокус F линзы.</p><p>Второй луч пустим из той же точки (острия стрелки) через оптический центр линзы. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.</p><p>Сами преломленные лучи после линзы являются расходящимися. Чтобы найти изображение, нужно найти точку пересечения их продолжений. Пересечение продолжения первого преломленного луча и второго луча (который не преломился) даст нам положение мнимого изображения острия стрелки. Эта точка будет находиться с той же стороны линзы, что и предмет.</p><p>Опустив перпендикуляр из полученной точки изображения острия на главную оптическую ось, мы найдем изображение основания стрелки. Соединив эти две точки, получим полное изображение предмета.</p><p>Полученное изображение будет мнимым (так как образовано пересечением продолжений лучей), прямым (неперевернутым) и уменьшенным по сравнению с предметом. Оно всегда располагается между линзой и ее мнимым фокусом F.</p><p><strong>Ответ:</strong> Изображение, даваемое рассеивающей линзой, строится с помощью двух лучей, выходящих из верхней точки предмета: луча, параллельного главной оптической оси (после преломления его продолжение проходит через мнимый фокус F), и луча, проходящего через оптический центр линзы (не преломляется). Точка пересечения продолжения первого луча и второго луча дает изображение верхней точки. В результате получается мнимое, прямое, уменьшенное изображение, расположенное между линзой и мнимым фокусом F.</p>"
          ]
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          #attributeCastCache: []
          #dateFormat: null
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          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "next" => array:2 [
      "refs" => "1613056"
      "type" => "task"
    ]
    "previous" => array:2 [
      "refs" => "1613054"
      "type" => "task"
    ]
    "book" => Illuminate\Database\Eloquent\Collection {#1129
      #items: array:1 [
        0 => App\Models\Book {#1083
          #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" => 3654
            "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 {#1075
              #items: array:1 [
                0 => App\Models\Term {#1078
                  #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 [
                      "field_accusative_case" => "физику"
                      "field_creative_case" => "физикой"
                      "field_dative_case" => "физике"
                      "field_genitive_case" => "физики"
                      "field_nominative_case" => "физика"
                      "field_prepositional_case" => "физике"
                    ]
                    "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 [
                      "field_accusative_case" => "физику"
                      "field_creative_case" => "физикой"
                      "field_dative_case" => "физике"
                      "field_genitive_case" => "физики"
                      "field_nominative_case" => "физика"
                      "field_prepositional_case" => "физике"
                    ]
                    "field_foreign_lang_name" => null
                    "field_short_name" => null
                    "field_subject_type" => "technical_subject"
                    "field_translit" => "fizika"
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
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                  #dispatchesEvents: []
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                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_class" => Illuminate\Database\Eloquent\Collection {#1085
              #items: array:1 [
                0 => App\Models\Term {#1081
                  #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" => 5457
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "8"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "восьмой"
                      "field_creative_case" => "восьмым"
                      "field_dative_case" => "восьмому"
                      "field_genitive_case" => "восьмого"
                      "field_nominative_case" => "восьмой"
                      "field_prepositional_case" => "восьмом"
                    ]
                    "field_translit" => "vosmoj"
                  ]
                  #original: array:6 [
                    "id" => 5457
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "8"
                    "field_cases" => array:6 [
                      "field_accusative_case" => "восьмой"
                      "field_creative_case" => "восьмым"
                      "field_dative_case" => "восьмому"
                      "field_genitive_case" => "восьмого"
                      "field_nominative_case" => "восьмой"
                      "field_prepositional_case" => "восьмом"
                    ]
                    "field_translit" => "vosmoj"
                  ]
                  #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 {#1079
              #items: array:1 [
                0 => App\Models\Term {#1082
                  #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 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_author" => Illuminate\Database\Eloquent\Collection {#1080
              #items: array:5 [
                0 => App\Models\Term {#1101
                  #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" => 4194
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Громов"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Сергей"
                    "field_patronymic" => "Васильевич"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 4194
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Громов"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Сергей"
                    "field_patronymic" => "Васильевич"
                    "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 => "*"
                  ]
                }
                1 => App\Models\Term {#1102
                  #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" => 5604
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Родина"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Надежда"
                    "field_patronymic" => "Александровна"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 5604
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Родина"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Надежда"
                    "field_patronymic" => "Александровна"
                    "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 => "*"
                  ]
                }
                2 => App\Models\Term {#1104
                  #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" => 3824
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Белага"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Виктория"
                    "field_patronymic" => "Владимировна"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 3824
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Белага"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Виктория"
                    "field_patronymic" => "Владимировна"
                    "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 => "*"
                  ]
                }
                3 => App\Models\Term {#1105
                  #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" => 5014
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Ломаченков"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Иван"
                    "field_patronymic" => "Алексеевич"
                    "field_surname_rp" => null
                  ]
                  #original: array:12 [
                    "id" => 5014
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Ломаченков"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Иван"
                    "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 => "*"
                  ]
                }
                4 => App\Models\Term {#1106
                  #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" => 5412
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Панебратцев"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Юрий"
                    "field_patronymic" => "Анатольевич"
                    "field_surname_rp" => "Панебратцева"
                  ]
                  #original: array:12 [
                    "id" => 5412
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Панебратцев"
                    "field_bio" => null
                    "field_degree_rp" => null
                    "field_foreign_lang_name" => null
                    "field_foreign_lang_patronymic" => null
                    "field_foreign_lang_surname" => null
                    "field_name" => "Юрий"
                    "field_patronymic" => "Анатольевич"
                    "field_surname_rp" => "Панебратцева"
                  ]
                  #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 {#1107
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_book_type" => Illuminate\Database\Eloquent\Collection {#1108
              #items: array:1 [
                0 => App\Models\Term {#1109
                  #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 [
                      "field_accusative_case" => "учебник"
                      "field_creative_case" => "учебником"
                      "field_dative_case" => "учебнику"
                      "field_genitive_case" => "учебника"
                      "field_nominative_case" => "учебник"
                      "field_prepositional_case" => "учебнике"
                    ]
                    "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 [
                      "field_accusative_case" => "учебник"
                      "field_creative_case" => "учебником"
                      "field_dative_case" => "учебнику"
                      "field_genitive_case" => "учебника"
                      "field_nominative_case" => "учебник"
                      "field_prepositional_case" => "учебнике"
                    ]
                    "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 {#1110
              #items: array:1 [
                0 => App\Models\Term {#1111
                  #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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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 {#1112
              #items: array:1 [
                0 => App\Models\Term {#1113
                  #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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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 {#1114
              #items: array:1 [
                0 => App\Models\Term {#1115
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:8 [
                    "id" => 4718
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "классический курс"
                    "field_cases" => null
                    "field_foreign_lang_series" => null
                    "field_transcription_eng" => null
                    "field_translit" => "klassicheskiy kurs"
                  ]
                  #original: array:8 [
                    "id" => 4718
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "классический курс"
                    "field_cases" => null
                    "field_foreign_lang_series" => null
                    "field_transcription_eng" => null
                    "field_translit" => "klassicheskiy kurs"
                  ]
                  #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_umk" => Illuminate\Database\Eloquent\Collection {#1116
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1117
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1118
              #items: array:1 [
                0 => App\Models\Term {#1119
                  #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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "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" => null
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1120
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1121
              #items: array:1 [
                0 => App\Models\Term {#1106}
              ]
              #escapeWhenCastingToString: false
            }
            "field_under_the_edition_degree" => null
            "field_cover_description" => null
            "field_publication_year" => "2018"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное пособие для общеобразовательных организаций"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "830"
            "field_priority" => null
            "field_default_folder" => "/fizika_08/gromov-u/"
            "field_isbn" => "978-5-09-052825-2"
            "field_cover" => array:1 [
              0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                "alt" => ""
                "width" => "1881"
                "height" => "2469"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1122
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1123
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1124
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_url" => "/8-klass/fizika/gromov-uchebnik"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1125
              #items: array:1 [
                0 => App\Models\Term {#1126
                  #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" => 49
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "синий"
                    "field_cases" => array:6 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "field_translit" => "siniy"
                  ]
                  #original: array:6 [
                    "id" => 49
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "синий"
                    "field_cases" => array:6 [
                      "field_accusative_case" => null
                      "field_creative_case" => null
                      "field_dative_case" => null
                      "field_genitive_case" => null
                      "field_nominative_case" => null
                      "field_prepositional_case" => null
                    ]
                    "field_translit" => "siniy"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
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                  #dateFormat: null
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                  #touches: []
                  +timestamps: true
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                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
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            "breadcrumbs" => array:3 [
              "class" => 379
              "subject" => 556
              "class_subject" => 492
            ]
          ]
          #original: array:50 [
            "id" => 3654
            "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 {#1075}
            "field_class" => Illuminate\Database\Eloquent\Collection {#1085}
            "field_publisher" => Illuminate\Database\Eloquent\Collection {#1079}
            "field_author" => Illuminate\Database\Eloquent\Collection {#1080}
            "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1107}
            "field_book_type" => Illuminate\Database\Eloquent\Collection {#1108}
            "field_country" => Illuminate\Database\Eloquent\Collection {#1110}
            "field_city" => Illuminate\Database\Eloquent\Collection {#1112}
            "field_series" => Illuminate\Database\Eloquent\Collection {#1114}
            "field_umk" => Illuminate\Database\Eloquent\Collection {#1116}
            "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1117}
            "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1118}
            "field_publication_number" => null
            "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1120}
            "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1121}
            "field_under_the_edition_degree" => null
            "field_cover_description" => null
            "field_publication_year" => "2018"
            "field_publication_year_until" => null
            "field_part" => ""
            "field_part_writing" => ""
            "field_second_foreign_language" => null
            "field_for_whom" => "Учебное пособие для общеобразовательных организаций"
            "field_allowed" => null
            "field_reserve_field" => null
            "field_link_to_source" => null
            "field_tasks_count" => "830"
            "field_priority" => null
            "field_default_folder" => "/fizika_08/gromov-u/"
            "field_isbn" => "978-5-09-052825-2"
            "field_cover" => array:1 [
              0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
            ]
            "field_cover_alts" => array:1 [
              0 => ""
            ]
            "field_covers" => array:1 [
              0 => array:4 [
                "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517"
                "alt" => ""
                "width" => "1881"
                "height" => "2469"
              ]
            ]
            "field_popular_book" => "0"
            "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1122}
            "field_new_book" => Illuminate\Database\Eloquent\Collection {#1123}
            "field_old_book" => Illuminate\Database\Eloquent\Collection {#1124}
            "field_url" => "/8-klass/fizika/gromov-uchebnik"
            "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1125}
            "field_metatags_title" => null
            "field_metatags_description" => null
            "field_h1" => null
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            "breadcrumbs" => array:3 [
              "class" => 379
              "subject" => 556
              "class_subject" => 492
            ]
          ]
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          #dateFormat: null
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          +timestamps: true
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          #visible: []
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          #guarded: array:1 [
            0 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "page" => Illuminate\Database\Eloquent\Collection {#1134
      #items: array:1 [
        0 => App\Models\BookPage {#1133
          #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" => 1613358
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_page_start" => "285"
            "field_url" => "/8-klass/fizika/gromov-uchebnik/page-285"
            "field_display_title" => "285"
            "field_folder" => "1"
            "field_image_name" => "285"
            "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1135
              #items: []
              #escapeWhenCastingToString: false
            }
            "field_weight" => "0"
            "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1136
              #items: array:1 [
                0 => App\Models\Book {#1083}
              ]
              #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 {#1137
              #items: []
              #escapeWhenCastingToString: false
            }
            "content" => Illuminate\Database\Eloquent\Collection {#1147
              #items: array:1 [
                0 => App\Models\Element {#1146
                  #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" => 1851069
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1148
                      #items: array:1 [
                        0 => App\Models\Edition {#1087}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "book_page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                    "img" => array:1 [
                      0 => array:5 [
                        "name" => "285-1.jpg"
                        "alt" => null
                        "width" => "1865"
                        "height" => 2548
                        "path" => "/media/fizika_08/gromov-u/0-1/285-1.webp?ts=1763478470"
                      ]
                    ]
                  ]
                  #original: array:6 [
                    "id" => 1851069
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "edition" => Illuminate\Database\Eloquent\Collection {#1148}
                    "book_page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                    "img" => array:1 [
                      0 => array:5 [
                        "name" => "285-1.jpg"
                        "alt" => null
                        "width" => "1865"
                        "height" => 2548
                        "path" => "/media/fizika_08/gromov-u/0-1/285-1.webp?ts=1763478470"
                      ]
                    ]
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
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                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "next" => array:2 [
              "refs" => "1613359"
              "type" => "book_page"
            ]
            "previous" => array:2 [
              "refs" => "1613357"
              "type" => "book_page"
            ]
            "tasks" => Illuminate\Database\Eloquent\Collection {#1238
              #items: array:4 [
                0 => App\Models\Task {#1248
                  #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" => 1613055
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-188"
                    "field_display_title" => "188"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249
                      #items: array:1 [
                        0 => App\Models\Term {#1036}
                      ]
                      #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 {#1250
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1252
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "content" => Illuminate\Database\Eloquent\Collection {#1253
                      #items: array:2 [
                        0 => App\Models\Element {#1086}
                        1 => App\Models\Element {#1093}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "next" => array:2 [
                      "refs" => "1613056"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
                      "refs" => "1613054"
                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1254
                      #items: array:1 [
                        0 => App\Models\Book {#1083}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #original: array:24 [
                    "id" => 1613055
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-188"
                    "field_display_title" => "188"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1249}
                    "field_metatags_title" => null
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                    "field_h1" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1250}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1251}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1252}
                    "content" => Illuminate\Database\Eloquent\Collection {#1253}
                    "next" => array:2 [
                      "refs" => "1613056"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
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                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1254}
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
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                  #dispatchesEvents: []
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                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                1 => App\Models\Task {#1255
                  #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" => 1613056
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-189"
                    "field_display_title" => "189"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256
                      #items: array:1 [
                        0 => App\Models\Term {#1036}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "content" => Illuminate\Database\Eloquent\Collection {#1261
                      #items: array:2 [
                        0 => App\Models\Element {#1270 …30}
                        1 => App\Models\Element {#1272 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "next" => array:2 [
                      "refs" => "1613057"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
                      "refs" => "1613055"
                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1267
                      #items: array:1 [
                        0 => App\Models\Book {#1083}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #original: array:24 [
                    "id" => 1613056
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-189"
                    "field_display_title" => "189"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1256}
                    "field_metatags_title" => null
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                    "field_h1" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1257}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1258}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1259}
                    "content" => Illuminate\Database\Eloquent\Collection {#1261}
                    "next" => array:2 [
                      "refs" => "1613057"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
                      "refs" => "1613055"
                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1267}
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
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                  #relations: []
                  #touches: []
                  +timestamps: true
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                2 => 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 [
                    "id" => 1613057
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-190"
                    "field_display_title" => "190"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260
                      #items: array:1 [
                        0 => App\Models\Term {#1036}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "field_description_bottom" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1269
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "content" => Illuminate\Database\Eloquent\Collection {#1264
                      #items: array:2 [
                        0 => App\Models\Element {#1282 …30}
                        1 => App\Models\Element {#1284 …30}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "next" => array:2 [
                      "refs" => "1613058"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
                      "refs" => "1613056"
                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1279
                      #items: array:1 [
                        0 => App\Models\Book {#1083}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #original: array:24 [
                    "id" => 1613057
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-190"
                    "field_display_title" => "190"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1260}
                    "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 {#1269}
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1265}
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1263}
                    "content" => Illuminate\Database\Eloquent\Collection {#1264}
                    "next" => array:2 [
                      "refs" => "1613058"
                      "type" => "task"
                    ]
                    "previous" => array:2 [
                      "refs" => "1613056"
                      "type" => "task"
                    ]
                    "book" => Illuminate\Database\Eloquent\Collection {#1279}
                    "page" => array:2 [
                      "refs" => "1613358"
                      "type" => "book_page"
                    ]
                  ]
                  #changes: []
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                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
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                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
                3 => App\Models\Task {#1274
                  #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" => 1613058
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_page_start" => "285"
                    "field_page_end" => null
                    "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-191"
                    "field_display_title" => "191"
                    "field_outside_task" => null
                    "field_task_type" => Illuminate\Database\Eloquent\Collection {#1266
                      #items: array:1 [
                        0 => App\Models\Term {#1036}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
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                    "breadcrumbs" => []
                    "edition_groups" => Illuminate\Database\Eloquent\Collection {#1281
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1277
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275
                      #items: array:1 [
                        0 => App\Models\Branch {#1034}
                      ]
                      #escapeWhenCastingToString: false
                    }
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}

№188 (с. 285)

Просмотр Редак-ть Редак-ть (переопр)

Условие. №188 (с. 285)

Редак-ть Редакция

скриншот условия

188. Постройте изображение, даваемое рассеивающей линзой в случае, показанном на рисунке 29.

Рис. 29

Решение. №188 (с. 285)

Редак-ть Редакция

Решение

Для построения изображения предмета (стрелки) в рассеивающей линзе необходимо построить изображение его верхней точки (острия). Изображение нижней точки, лежащей на главной оптической оси, также будет лежать на оси, под изображением верхней точки.

Для построения изображения острия стрелки проведем два луча, ход которых известен. Первый луч пустим из острия стрелки параллельно главной оптической оси. После прохождения через рассеивающую линзу он пойдет так, что его продолжение, проведенное в обратную сторону (к предмету), пройдет через мнимый фокус F линзы.

Второй луч пустим из той же точки (острия стрелки) через оптический центр линзы. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.

Сами преломленные лучи после линзы являются расходящимися. Чтобы найти изображение, нужно найти точку пересечения их продолжений. Пересечение продолжения первого преломленного луча и второго луча (который не преломился) даст нам положение мнимого изображения острия стрелки. Эта точка будет находиться с той же стороны линзы, что и предмет.

Опустив перпендикуляр из полученной точки изображения острия на главную оптическую ось, мы найдем изображение основания стрелки. Соединив эти две точки, получим полное изображение предмета.

Полученное изображение будет мнимым (так как образовано пересечением продолжений лучей), прямым (неперевернутым) и уменьшенным по сравнению с предметом. Оно всегда располагается между линзой и ее мнимым фокусом F.

Ответ: Изображение, даваемое рассеивающей линзой, строится с помощью двух лучей, выходящих из верхней точки предмета: луча, параллельного главной оптической оси (после преломления его продолжение проходит через мнимый фокус F), и луча, проходящего через оптический центр линзы (не преломляется). Точка пересечения продолжения первого луча и второго луча дает изображение верхней точки. В результате получается мнимое, прямое, уменьшенное изображение, расположенное между линзой и мнимым фокусом F.