Номер 2, страница 46, часть 3 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев

Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.

Тип: рабочая тетрадь

Издательство: Просвещение

Год издания: 2021 - 2026

Часть: 3

Цвет обложки: синий

ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)

Часть 3. Глава 8. Оптика. Параграф 48. Построение изображений, создаваемых тонкими собирающими линзами - номер 2, страница 46.

App\Models\Task {#1030 // resources/views/models/task/default.blade.php
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                    "field_cover" => array:3 [ …3]
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                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2}
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                            "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 {#1175
                      #items: array:4 [
                        0 => App\Models\Term {#1176
                          #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" => 4180
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Грачев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Александр"
                            "field_patronymic" => "Васильевич"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4180
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Грачев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Александр"
                            "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 {#1177
                          #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" => 5484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Погожев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Владимир"
                            "field_patronymic" => "Александрович"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 5484
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Погожев"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Владимир"
                            "field_patronymic" => "Александрович"
                            "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 {#1178
                          #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" => 3888
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Боков"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Павел"
                            "field_patronymic" => "Юрьевич"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 3888
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Боков"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Павел"
                            "field_patronymic" => "Юрьевич"
                            "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 {#1179
                          #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" => 4007
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Вишнякова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Екатерина"
                            "field_patronymic" => "Анатольевна"
                            "field_surname_rp" => null
                          ]
                          #original: array:12 [
                            "id" => 4007
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Вишнякова"
                            "field_bio" => null
                            "field_degree_rp" => null
                            "field_foreign_lang_name" => null
                            "field_foreign_lang_patronymic" => null
                            "field_foreign_lang_surname" => null
                            "field_name" => "Екатерина"
                            "field_patronymic" => "Анатольевна"
                            "field_surname_rp" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1180
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1181
                      #items: array:1 [
                        0 => App\Models\Term {#1182
                          #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" => 6736
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "рабочая тетрадь"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => "рабочие тетради"
                            "field_short_name" => "рт"
                            "field_short_name_foreign" => null
                            "field_translit" => "rabochaya tetrad"
                          ]
                          #original: array:10 [
                            "id" => 6736
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "рабочая тетрадь"
                            "field_book_type_foreign" => null
                            "field_cases" => array:6 [ …6]
                            "field_plural_form" => "рабочие тетради"
                            "field_short_name" => "рт"
                            "field_short_name_foreign" => null
                            "field_translit" => "rabochaya tetrad"
                          ]
                          #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 {#1183
                      #items: array:1 [
                        0 => App\Models\Term {#1184
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #original: array:6 [
                            "id" => 9
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Россия"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "rossiya"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1185
                      #items: array:1 [
                        0 => App\Models\Term {#1186
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #original: array:6 [
                            "id" => 15
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "Москва"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "moskva"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1187
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1188
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190
                      #items: array:1 [
                        0 => App\Models\Term {#1191
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #original: array:10 [
                            "id" => 6706
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "ФГОС (старый)"
                            "field_cases" => array:6 [ …6]
                            "field_color" => null
                            "field_end_year" => "2022"
                            "field_start_year" => "2019"
                            "field_translit" => "fgos-old"
                            "field_type" => null
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_publication_number" => "6"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192
                      #items: array:1 [
                        0 => App\Models\Term {#1193
                          #connection: "mysql"
                          #table: "terms"
                          #primaryKey: "id"
                          #keyType: "int"
                          +incrementing: false
                          #with: []
                          #withCount: []
                          +preventsLazyLoading: false
                          #perPage: 15
                          +exists: true
                          +wasRecentlyCreated: false
                          #escapeWhenCastingToString: false
                          #attributes: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #original: array:6 [
                            "id" => 33
                            "created_at" => "2026-04-10 13:58:26"
                            "updated_at" => null
                            "name" => "стереотипное"
                            "field_cases" => array:6 [ …6]
                            "field_translit" => "stereotipnoe"
                          ]
                          #changes: []
                          #casts: []
                          #classCastCache: []
                          #attributeCastCache: []
                          #dateFormat: null
                          #appends: []
                          #dispatchesEvents: []
                          #observables: []
                          #relations: []
                          #touches: []
                          +timestamps: true
                          +usesUniqueIds: false
                          #hidden: []
                          #visible: []
                          #fillable: []
                          #guarded: array:1 [
                            0 => "*"
                          ]
                        }
                      ]
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1194
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2021"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2, 3"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "594"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/grachev-rt/"
                    "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)"
                    "field_cover" => array:3 [
                      0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248"
                      1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248"
                      2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248"
                    ]
                    "field_cover_alts" => array:3 [
                      0 => ""
                      1 => ""
                      2 => ""
                    ]
                    "field_covers" => array:3 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2293"
                        "height" => "2989"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2265"
                        "height" => "3003"
                      ]
                      2 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2241"
                        "height" => "2999"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197
                      #items: []
                      #escapeWhenCastingToString: false
                    }
                    "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198
                      #items: array:1 [
                        0 => App\Models\Term {#1199
                          #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 [ …6]
                            "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 [ …6]
                            "field_translit" => "siniy"
                          ]
                          #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
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #original: array:50 [
                    "id" => 1203
                    "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 {#1170}
                    "field_class" => Illuminate\Database\Eloquent\Collection {#1171}
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173}
                    "field_author" => Illuminate\Database\Eloquent\Collection {#1175}
                    "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1180}
                    "field_book_type" => Illuminate\Database\Eloquent\Collection {#1181}
                    "field_country" => Illuminate\Database\Eloquent\Collection {#1183}
                    "field_city" => Illuminate\Database\Eloquent\Collection {#1185}
                    "field_series" => Illuminate\Database\Eloquent\Collection {#1187}
                    "field_umk" => Illuminate\Database\Eloquent\Collection {#1188}
                    "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189}
                    "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190}
                    "field_publication_number" => "6"
                    "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192}
                    "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1194}
                    "field_under_the_edition_degree" => null
                    "field_cover_description" => null
                    "field_publication_year" => "2021"
                    "field_publication_year_until" => null
                    "field_part" => "1, 2, 3"
                    "field_part_writing" => "Часть"
                    "field_second_foreign_language" => null
                    "field_for_whom" => "Учебное издание"
                    "field_allowed" => null
                    "field_reserve_field" => null
                    "field_link_to_source" => null
                    "field_tasks_count" => "594"
                    "field_priority" => null
                    "field_default_folder" => "/fizika_09/grachev-rt/"
                    "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)"
                    "field_cover" => array:3 [
                      0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248"
                      1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248"
                      2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248"
                    ]
                    "field_cover_alts" => array:3 [
                      0 => ""
                      1 => ""
                      2 => ""
                    ]
                    "field_covers" => array:3 [
                      0 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2293"
                        "height" => "2989"
                      ]
                      1 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2265"
                        "height" => "3003"
                      ]
                      2 => array:4 [
                        "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248"
                        "alt" => ""
                        "width" => "2241"
                        "height" => "2999"
                      ]
                    ]
                    "field_popular_book" => "0"
                    "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195}
                    "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196}
                    "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197}
                    "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad"
                    "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198}
                    "field_metatags_title" => null
                    "field_metatags_description" => null
                    "field_h1" => null
                    "field_description_top" => null
                    "field_description_bottom" => null
                    "breadcrumbs" => array:3 [
                      "class" => 380
                      "subject" => 556
                      "class_subject" => 493
                    ]
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1200
              #items: []
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1434847
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => null
            "field_branch_order" => "3"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169}
            "field_page_start" => "3"
            "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 {#1202}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1200}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        1 => App\Models\Branch {#1201
          #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" => 1434852
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Оптика"
            "field_branch_order" => "8"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206
              #items: array:1 [
                0 => App\Models\Term {#1203
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #original: array:7 [
                    "id" => 29
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Глава"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => null
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "15"
            "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 {#1205
              #items: array:1 [
                0 => App\Models\Book {#1168}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204
              #items: array:1 [
                0 => App\Models\Branch {#1034}
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1434852
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Оптика"
            "field_branch_order" => "8"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206}
            "field_page_start" => "15"
            "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 {#1205}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204}
          ]
          #changes: []
          #casts: []
          #classCastCache: []
          #attributeCastCache: []
          #dateFormat: null
          #appends: []
          #dispatchesEvents: []
          #observables: []
          #relations: []
          #touches: []
          +timestamps: true
          +usesUniqueIds: false
          #hidden: []
          #visible: []
          #fillable: []
          #guarded: array:1 [
            0 => "*"
          ]
        }
        2 => App\Models\Branch {#1207
          #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" => 1434862
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Построение изображений, создаваемых тонкими собирающими линзами"
            "field_branch_order" => "48"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211
              #items: array:1 [
                0 => App\Models\Term {#1208
                  #connection: "mysql"
                  #table: "terms"
                  #primaryKey: "id"
                  #keyType: "int"
                  +incrementing: false
                  #with: []
                  #withCount: []
                  +preventsLazyLoading: false
                  #perPage: 15
                  +exists: true
                  +wasRecentlyCreated: false
                  #escapeWhenCastingToString: false
                  #attributes: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #original: array:7 [
                    "id" => 32
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "name" => "Параграф"
                    "field_cases" => array:6 [ …6]
                    "field_page_check_not_needed" => null
                    "field_short_name" => "§"
                  ]
                  #changes: []
                  #casts: []
                  #classCastCache: []
                  #attributeCastCache: []
                  #dateFormat: null
                  #appends: []
                  #dispatchesEvents: []
                  #observables: []
                  #relations: []
                  #touches: []
                  +timestamps: true
                  +usesUniqueIds: false
                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
            "field_page_start" => "45"
            "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 {#1210
              #items: array:1 [
                0 => App\Models\Book {#1168}
              ]
              #escapeWhenCastingToString: false
            }
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1255
              #items: array:1 [
                0 => App\Models\Branch {#1209
                  #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" => 1434852
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Оптика"
                    "field_branch_order" => "8"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 …2}
                    "field_page_start" => "15"
                    "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
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                    "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 {#1214 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 …2}
                  ]
                  #original: array:24 [
                    "id" => 1434852
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "field_display_title" => "Оптика"
                    "field_branch_order" => "8"
                    "field_url" => null
                    "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1213 …2}
                    "field_page_start" => "15"
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                    "field_branch_expanded" => "0"
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                    "field_branch_title_in_content" => "0"
                    "field_navigation_title" => null
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                    "field_metatags_description" => null
                    "field_h1" => null
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                    "field_branch_cover" => []
                    "field_branch_covers" => []
                    "book" => Illuminate\Database\Eloquent\Collection {#1214 …2}
                    "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 …2}
                  ]
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                  #attributeCastCache: []
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                  #hidden: []
                  #visible: []
                  #fillable: []
                  #guarded: array:1 [
                    0 => "*"
                  ]
                }
              ]
              #escapeWhenCastingToString: false
            }
          ]
          #original: array:24 [
            "id" => 1434862
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "field_display_title" => "Построение изображений, создаваемых тонкими собирающими линзами"
            "field_branch_order" => "48"
            "field_url" => null
            "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211}
            "field_page_start" => "45"
            "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 {#1210}
            "branch_parent" => Illuminate\Database\Eloquent\Collection {#1255}
          ]
          #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 => "*"
          ]
        }
      ]
      #escapeWhenCastingToString: false
    }
    "content" => Illuminate\Database\Eloquent\Collection {#1112
      #items: array:2 [
        0 => App\Models\Element {#1144
          #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" => 1698694
            "created_at" => "2026-04-10 13:58:26"
            "updated_at" => null
            "edition" => Illuminate\Database\Eloquent\Collection {#1135
              #items: array:1 [
                0 => App\Models\Edition {#1143
                  #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" => 6173
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2}
                    "field_content_source" => null
                  ]
                  #original: array:21 [
                    "id" => 6173
                    "created_at" => "2026-04-10 13:58:26"
                    "updated_at" => null
                    "title" => "Условие"
                    "field_order" => "1"
                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2}
                    "field_content_type" => "free"
                    "field_content_mode" => "text, image"
                    "field_page_content_mode" => "image"
                    "field_content_text_checked" => null
                    "field_page_content_text_checked" => "0"
                    "field_solution_author" => "Автор"
                    "field_moderator" => "stas"
                    "field_edition_type" => "statement"
                    "field_root_dir" => "0-"
                    "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2}
                    "field_comment" => null
                    "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2}
                    "field_process_formula" => "katex"
                    "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2}
                    "field_content_source" => null
                  ]
                  #changes: []
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                  #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" => "1435306"
              "type" => "task"
            ]
            "text" => "<p><strong>2.</strong> Зачеркните в пунктах а—е неверные утверждения.</p><p>Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.</p><p>Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.</p>"
            "img" => array:1 [
              0 => array:5 [
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                "height" => 587
                "path" => "/media/fizika_09/grachev-rt/0-48/2-1.webp?ts=1759402878"
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            "created_at" => "2026-04-10 13:58:26"
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            "task" => array:2 [
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              "type" => "task"
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            "text" => "<p><strong>2.</strong> Зачеркните в пунктах а—е неверные утверждения.</p><p>Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.</p><p>Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.</p>"
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                    "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134 …2}
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            "text" => "<p><strong>Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.</strong></p> <p>В геометрической оптике существует правило знаков, согласно которому расстояние от главной плоскости линзы до изображения (обозначим его $f'$) считается:</p> <ul> <li>Положительным ($f' &gt; 0$), если изображение является действительным (реальным). Действительное изображение формируется на пересечении самих преломленных лучей.</li> <li>Отрицательным ($f' &lt; 0$), если изображение является мнимым. Мнимое изображение формируется на пересечении продолжений преломленных лучей.</li> </ul> <p>Проанализируем предложенные варианты:</p> <p>а) <strong>уменьшенным</strong>: Изображение может быть уменьшенным и при этом действительным (например, когда предмет находится за двойным фокусным расстоянием от собирающей линзы, $f'&gt;0$). Также оно может быть уменьшенным и мнимым (любое изображение в рассеивающей линзе, $f'&lt;0$). Таким образом, характеристика "уменьшенное" не определяет однозначно знак расстояния до изображения. Это неверное утверждение как необходимое и достаточное условие.</p> <p>б) <strong>мнимым</strong>: Согласно правилу знаков, если изображение мнимое, то расстояние до него считается отрицательным. Это верное утверждение.</p> <p>в) <strong>перевёрнутым</strong>: Перевёрнутое изображение, создаваемое одиночной линзой, всегда является действительным. Для действительного изображения расстояние $f'$ положительно. Следовательно, это неверное утверждение.</p> <p>Задание требует зачеркнуть (т.е. определить как неверные) утверждения, которые не являются правильным условием для отрицательного расстояния до изображения.</p> <p><strong>Ответ:</strong> Неверными утверждениями являются <strong>а) уменьшенным</strong> и <strong>в) перевёрнутым</strong>.</p> <hr> <p><strong>Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.</strong></p> <p><strong>Дано:</strong></p> <p>Положение предмета: $d = 2F$</p> <p>(где $d$ - расстояние от предмета до линзы, $F$ - фокусное расстояние линзы). По умолчанию для такого расположения предмета рассматривается собирающая линза ($F &gt; 0$).</p> <p><strong>Найти:</strong></p> <p>Характеристики изображения.</p> <p><strong>Решение:</strong></p> <p>Для определения характеристик изображения воспользуемся формулой тонкой линзы:</p> <p>$ \frac{1}{d} + \frac{1}{f'} = \frac{1}{F} $</p> <p>где $f'$ - расстояние от линзы до изображения.</p> <p>1. Найдем расстояние до изображения $f'$. Подставим $d = 2F$ в формулу:</p> <p>$ \frac{1}{2F} + \frac{1}{f'} = \frac{1}{F} $</p> <p>Перенесем $ \frac{1}{2F} $ в правую часть:</p> <p>$ \frac{1}{f'} = \frac{1}{F} - \frac{1}{2F} = \frac{2-1}{2F} = \frac{1}{2F} $</p> <p>Отсюда $f' = 2F$.</p> <p>Так как $f' &gt; 0$, изображение является <strong>действительным</strong>. Следовательно, утверждение (б) верно, а утверждение (а) <strong>мнимым</strong> - неверно.</p> <p>2. Определим линейное увеличение $Г$:</p> <p>$ Г = -\frac{f'}{d} $</p> <p>Подставим известные значения $d=2F$ и $f'=2F$:</p> <p>$ Г = -\frac{2F}{2F} = -1 $</p> <p>Проанализируем полученное значение увеличения:</p> <ul> <li>Знак "$–$" означает, что изображение <strong>перевёрнутое</strong>. Следовательно, утверждение (е) верно, а утверждение (д) <strong>прямым</strong> - неверно.</li> <li>Модуль увеличения $|Г| = 1$ означает, что размер изображения равен размеру предмета. Следовательно, утверждения (в) <strong>увеличенным</strong> и (г) <strong>уменьшенным</strong> являются неверными.</li> </ul> <p>Таким образом, верными характеристиками изображения являются: действительное, равное по размеру, перевёрнутое. Задание требует определить неверные утверждения из списка.</p> <p><strong>Ответ:</strong> Неверными утверждениями являются <strong>а) мнимым</strong>, <strong>в) увеличенным</strong>, <strong>г) уменьшенным</strong> и <strong>д) прямым</strong>.</p>"
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            "task" => array:2 [
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            "text" => "<p><strong>Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.</strong></p> <p>В геометрической оптике существует правило знаков, согласно которому расстояние от главной плоскости линзы до изображения (обозначим его $f'$) считается:</p> <ul> <li>Положительным ($f' &gt; 0$), если изображение является действительным (реальным). Действительное изображение формируется на пересечении самих преломленных лучей.</li> <li>Отрицательным ($f' &lt; 0$), если изображение является мнимым. Мнимое изображение формируется на пересечении продолжений преломленных лучей.</li> </ul> <p>Проанализируем предложенные варианты:</p> <p>а) <strong>уменьшенным</strong>: Изображение может быть уменьшенным и при этом действительным (например, когда предмет находится за двойным фокусным расстоянием от собирающей линзы, $f'&gt;0$). Также оно может быть уменьшенным и мнимым (любое изображение в рассеивающей линзе, $f'&lt;0$). Таким образом, характеристика "уменьшенное" не определяет однозначно знак расстояния до изображения. Это неверное утверждение как необходимое и достаточное условие.</p> <p>б) <strong>мнимым</strong>: Согласно правилу знаков, если изображение мнимое, то расстояние до него считается отрицательным. Это верное утверждение.</p> <p>в) <strong>перевёрнутым</strong>: Перевёрнутое изображение, создаваемое одиночной линзой, всегда является действительным. Для действительного изображения расстояние $f'$ положительно. Следовательно, это неверное утверждение.</p> <p>Задание требует зачеркнуть (т.е. определить как неверные) утверждения, которые не являются правильным условием для отрицательного расстояния до изображения.</p> <p><strong>Ответ:</strong> Неверными утверждениями являются <strong>а) уменьшенным</strong> и <strong>в) перевёрнутым</strong>.</p> <hr> <p><strong>Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.</strong></p> <p><strong>Дано:</strong></p> <p>Положение предмета: $d = 2F$</p> <p>(где $d$ - расстояние от предмета до линзы, $F$ - фокусное расстояние линзы). По умолчанию для такого расположения предмета рассматривается собирающая линза ($F &gt; 0$).</p> <p><strong>Найти:</strong></p> <p>Характеристики изображения.</p> <p><strong>Решение:</strong></p> <p>Для определения характеристик изображения воспользуемся формулой тонкой линзы:</p> <p>$ \frac{1}{d} + \frac{1}{f'} = \frac{1}{F} $</p> <p>где $f'$ - расстояние от линзы до изображения.</p> <p>1. Найдем расстояние до изображения $f'$. Подставим $d = 2F$ в формулу:</p> <p>$ \frac{1}{2F} + \frac{1}{f'} = \frac{1}{F} $</p> <p>Перенесем $ \frac{1}{2F} $ в правую часть:</p> <p>$ \frac{1}{f'} = \frac{1}{F} - \frac{1}{2F} = \frac{2-1}{2F} = \frac{1}{2F} $</p> <p>Отсюда $f' = 2F$.</p> <p>Так как $f' &gt; 0$, изображение является <strong>действительным</strong>. Следовательно, утверждение (б) верно, а утверждение (а) <strong>мнимым</strong> - неверно.</p> <p>2. Определим линейное увеличение $Г$:</p> <p>$ Г = -\frac{f'}{d} $</p> <p>Подставим известные значения $d=2F$ и $f'=2F$:</p> <p>$ Г = -\frac{2F}{2F} = -1 $</p> <p>Проанализируем полученное значение увеличения:</p> <ul> <li>Знак "$–$" означает, что изображение <strong>перевёрнутое</strong>. Следовательно, утверждение (е) верно, а утверждение (д) <strong>прямым</strong> - неверно.</li> <li>Модуль увеличения $|Г| = 1$ означает, что размер изображения равен размеру предмета. Следовательно, утверждения (в) <strong>увеличенным</strong> и (г) <strong>уменьшенным</strong> являются неверными.</li> </ul> <p>Таким образом, верными характеристиками изображения являются: действительное, равное по размеру, перевёрнутое. Задание требует определить неверные утверждения из списка.</p> <p><strong>Ответ:</strong> Неверными утверждениями являются <strong>а) мнимым</strong>, <strong>в) увеличенным</strong>, <strong>г) уменьшенным</strong> и <strong>д) прямым</strong>.</p>"
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№2 (с. 46)
Условие. №2 (с. 46)
скриншот условия
Физика, 9 класс рабочая тетрадь, авторы: Грачев Александр Васильевич, Погожев Владимир Александрович, Боков Павел Юрьевич, Вишнякова Екатерина Анатольевна, издательство Просвещение, Москва, 2021, Часть 3, страница 46, номер 2, Условие

2. Зачеркните в пунктах а—е неверные утверждения.

Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.

Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.

Решение. №2 (с. 46)

Расстояние от главной плоскости линзы до изображения считают отрицательным, если изображение точечного источника света в линзе является: а) уменьшенным; б) мнимым; в) перевёрнутым.

В геометрической оптике существует правило знаков, согласно которому расстояние от главной плоскости линзы до изображения (обозначим его $f'$) считается:

  • Положительным ($f' > 0$), если изображение является действительным (реальным). Действительное изображение формируется на пересечении самих преломленных лучей.
  • Отрицательным ($f' < 0$), если изображение является мнимым. Мнимое изображение формируется на пересечении продолжений преломленных лучей.

Проанализируем предложенные варианты:

а) уменьшенным: Изображение может быть уменьшенным и при этом действительным (например, когда предмет находится за двойным фокусным расстоянием от собирающей линзы, $f'>0$). Также оно может быть уменьшенным и мнимым (любое изображение в рассеивающей линзе, $f'<0$). Таким образом, характеристика "уменьшенное" не определяет однозначно знак расстояния до изображения. Это неверное утверждение как необходимое и достаточное условие.

б) мнимым: Согласно правилу знаков, если изображение мнимое, то расстояние до него считается отрицательным. Это верное утверждение.

в) перевёрнутым: Перевёрнутое изображение, создаваемое одиночной линзой, всегда является действительным. Для действительного изображения расстояние $f'$ положительно. Следовательно, это неверное утверждение.

Задание требует зачеркнуть (т.е. определить как неверные) утверждения, которые не являются правильным условием для отрицательного расстояния до изображения.

Ответ: Неверными утверждениями являются а) уменьшенным и в) перевёрнутым.


Если перпендикулярная главной оптической оси светящаяся стрелка находится на двойном фокусном расстоянии от тонкой сферической линзы, то её изображение будет: а) мнимым; б) действительным; в) увеличенным; г) уменьшенным; д) прямым; е) перевёрнутым.

Дано:

Положение предмета: $d = 2F$

(где $d$ - расстояние от предмета до линзы, $F$ - фокусное расстояние линзы). По умолчанию для такого расположения предмета рассматривается собирающая линза ($F > 0$).

Найти:

Характеристики изображения.

Решение:

Для определения характеристик изображения воспользуемся формулой тонкой линзы:

$ \frac{1}{d} + \frac{1}{f'} = \frac{1}{F} $

где $f'$ - расстояние от линзы до изображения.

1. Найдем расстояние до изображения $f'$. Подставим $d = 2F$ в формулу:

$ \frac{1}{2F} + \frac{1}{f'} = \frac{1}{F} $

Перенесем $ \frac{1}{2F} $ в правую часть:

$ \frac{1}{f'} = \frac{1}{F} - \frac{1}{2F} = \frac{2-1}{2F} = \frac{1}{2F} $

Отсюда $f' = 2F$.

Так как $f' > 0$, изображение является действительным. Следовательно, утверждение (б) верно, а утверждение (а) мнимым - неверно.

2. Определим линейное увеличение $Г$:

$ Г = -\frac{f'}{d} $

Подставим известные значения $d=2F$ и $f'=2F$:

$ Г = -\frac{2F}{2F} = -1 $

Проанализируем полученное значение увеличения:

  • Знак "$–$" означает, что изображение перевёрнутое. Следовательно, утверждение (е) верно, а утверждение (д) прямым - неверно.
  • Модуль увеличения $|Г| = 1$ означает, что размер изображения равен размеру предмета. Следовательно, утверждения (в) увеличенным и (г) уменьшенным являются неверными.

Таким образом, верными характеристиками изображения являются: действительное, равное по размеру, перевёрнутое. Задание требует определить неверные утверждения из списка.

Ответ: Неверными утверждениями являются а) мнимым, в) увеличенным, г) уменьшенным и д) прямым.

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