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Номер 5, страница 52, 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)
Популярные ГДЗ в 9 классе
Часть 3. Глава 8. Оптика. Параграф 49. Построение изображений, создаваемых тонкими рассеивающими линзами - номер 5, страница 52.
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" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "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" => 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 {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #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" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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" => "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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 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 {#1042 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:4 [ …4] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 #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 [ …4] 1 => array:4 [ …4] 2 => array:4 [ …4] ] "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" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ …1] #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 {#1042} "field_class" => Illuminate\Database\Eloquent\Collection {#1044} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "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 {#1061} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067} "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 [ …4] 1 => array:4 [ …4] 2 => array:4 [ …4] ] "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" => "/9-klass/fizika/grachev-rabochaya-tetrad" "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" => 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 {#1073 #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 {#1039} "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 {#1040} "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 {#1155 #items: array:3 [ 0 => App\Models\Branch {#1165 #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" => 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 #items: array:1 [ 0 => App\Models\Term {#1166 #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" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #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" => "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 #items: array:1 [ 0 => App\Models\Book {#1168 #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" => 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 #items: array:1 [ 0 => App\Models\Term {#1167 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ 0 => App\Models\Term {#1172 #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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #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 {#1173 #items: array:1 [ 0 => App\Models\Term {#1174 #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 {#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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => 1434863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "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" => "51" "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 #items: array:1 [ …1] #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 {#1214 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ …1] #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 {#1213} "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 {#1214} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "51" "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: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1112 #items: array: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" => 1698715 "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 #items: array:1 [ …1] #escapeWhenCastingToString: false } "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 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "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} "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} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139} "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" => "1435327" "type" => "task" ] "text" => "<p><strong>5.</strong> На рис. 66 показаны тонкая рассеивающая линза и её главные фокусы. Постройте изображение $S'$ точечного источника света $\text{S}$.</p><p>Рис. 66</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1906" "height" => 695 "path" => "/media/fizika_09/grachev-rt/0-49/5-1.webp?ts=1759402878" ] ] ] #original: array:7 [ "id" => 1698715 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1135} "task" => array:2 [ "refs" => "1435327" "type" => "task" ] "text" => "<p><strong>5.</strong> На рис. 66 показаны тонкая рассеивающая линза и её главные фокусы. Постройте изображение $S'$ точечного источника света $\text{S}$.</p><p>Рис. 66</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1906" "height" => 695 "path" => "/media/fizika_09/grachev-rt/0-49/5-1.webp?ts=1759402878" ] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Element {#1137 #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" => 1734701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123 #items: array:1 [ 0 => App\Models\Edition {#1136 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132 #items: [] …1 } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1134} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1131} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1132 …1} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1435327" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для построения изображения $S'$ точечного источника света $S$ в рассеивающей линзе необходимо использовать ход как минимум двух характерных лучей, исходящих из точки $S$. Изображение будет находиться в точке пересечения продолжений этих лучей после их преломления в линзе.</p><p>1. Первый луч (на рисунке показан синим цветом) проведем из точки $S$ через оптический центр линзы $O$. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.</p><p>2. Второй луч (на рисунке показан красным цветом) проведем из точки $S$ параллельно главной оптической оси до пересечения с плоскостью линзы. После преломления в рассеивающей линзе этот луч пойдет так, что его продолжение (показано красной пунктирной линией) пройдет через передний главный фокус $F$ линзы (тот, что находится с той же стороны от линзы, что и источник $S$).</p><p>3. Точка $S'$, в которой пересекаются первый луч (прошедший через оптический центр) и продолжение второго преломленного луча, и является искомым изображением источника $S$. Так как изображение образовано пересечением не самих лучей, а их продолжений, оно является мнимым.</p><p>Графическое построение показано на рисунке ниже.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения S' точечного источника S в рассеивающей линзе."></p><p><strong>Ответ:</strong></p><p>Построение изображения $S'$ точечного источника света $S$ показано на рисунке. Изображение является мнимым (получено на пересечении продолжений лучей), прямым (неперевернутым относительно главной оптической оси) и уменьшенным. Оно расположено с той же стороны от линзы, что и сам источник, между фокусом $F$ и оптическим центром $O$.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения S' точечного источника S в рассеивающей линзе."></p>" ] #original: array:6 [ "id" => 1734701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1123} "task" => array:2 [ "refs" => "1435327" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для построения изображения $S'$ точечного источника света $S$ в рассеивающей линзе необходимо использовать ход как минимум двух характерных лучей, исходящих из точки $S$. Изображение будет находиться в точке пересечения продолжений этих лучей после их преломления в линзе.</p><p>1. Первый луч (на рисунке показан синим цветом) проведем из точки $S$ через оптический центр линзы $O$. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.</p><p>2. Второй луч (на рисунке показан красным цветом) проведем из точки $S$ параллельно главной оптической оси до пересечения с плоскостью линзы. После преломления в рассеивающей линзе этот луч пойдет так, что его продолжение (показано красной пунктирной линией) пройдет через передний главный фокус $F$ линзы (тот, что находится с той же стороны от линзы, что и источник $S$).</p><p>3. Точка $S'$, в которой пересекаются первый луч (прошедший через оптический центр) и продолжение второго преломленного луча, и является искомым изображением источника $S$. Так как изображение образовано пересечением не самих лучей, а их продолжений, оно является мнимым.</p><p>Графическое построение показано на рисунке ниже.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения S' точечного источника S в рассеивающей линзе."></p><p><strong>Ответ:</strong></p><p>Построение изображения $S'$ точечного источника света $S$ показано на рисунке. Изображение является мнимым (получено на пересечении продолжений лучей), прямым (неперевернутым относительно главной оптической оси) и уменьшенным. Оно расположено с той же стороны от линзы, что и сам источник, между фокусом $F$ и оптическим центром $O$.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения S' точечного источника S в рассеивающей линзе."></p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435328" "type" => "task" ] "previous" => array:2 [ "refs" => "1435326" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\BookPage {#1116 #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" => 1435687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-52" "field_display_title" => "52" "field_folder" => "3" "field_image_name" => "52" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1165} ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1128 #items: array:1 [ 0 => App\Models\Book {#1168} ] #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 {#1127 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Element {#1118 #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" => 1699074 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1151 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1699074 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1151 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435688" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435686" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1350 #items: array:3 [ 0 => App\Models\Task {#1360 #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" => 1435326 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1361 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1362 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1363 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1364 …2} "content" => Illuminate\Database\Eloquent\Collection {#1366 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1372 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435326 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1361 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1362 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1363 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1364 …2} "content" => Illuminate\Database\Eloquent\Collection {#1366 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1372 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1367 #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" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1365 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1374 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1370 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1368 …2} "content" => Illuminate\Database\Eloquent\Collection {#1371 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1369 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1365 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1374 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1370 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1368 …2} "content" => Illuminate\Database\Eloquent\Collection {#1371 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1369 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1379 #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" => 1435328 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1380 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1381 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1382 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1383 …2} "content" => Illuminate\Database\Eloquent\Collection {#1385 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1391 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435328 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1380 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1381 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1382 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1383 …2} "content" => Illuminate\Database\Eloquent\Collection {#1385 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1391 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1435687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-52" "field_display_title" => "52" "field_folder" => "3" "field_image_name" => "52" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1128} "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 {#1127} "content" => Illuminate\Database\Eloquent\Collection {#1150} "next" => array:2 [ "refs" => "1435688" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435686" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1350} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1076} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1155} "content" => Illuminate\Database\Eloquent\Collection {#1112} "next" => array:2 [ "refs" => "1435328" "type" => "task" ] "previous" => array:2 [ "refs" => "1435326" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146} "page" => array:2 [ "refs" => "1435687" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№5 (с. 52)
Условие. №5 (с. 52)
скриншот условия
5. На рис. 66 показаны тонкая рассеивающая линза и её главные фокусы. Постройте изображение $S'$ точечного источника света $\text{S}$.
Рис. 66
Решение. №5 (с. 52)
Решение
Для построения изображения $S'$ точечного источника света $S$ в рассеивающей линзе необходимо использовать ход как минимум двух характерных лучей, исходящих из точки $S$. Изображение будет находиться в точке пересечения продолжений этих лучей после их преломления в линзе.
1. Первый луч (на рисунке показан синим цветом) проведем из точки $S$ через оптический центр линзы $O$. Этот луч проходит через линзу, не преломляясь и не меняя своего направления.
2. Второй луч (на рисунке показан красным цветом) проведем из точки $S$ параллельно главной оптической оси до пересечения с плоскостью линзы. После преломления в рассеивающей линзе этот луч пойдет так, что его продолжение (показано красной пунктирной линией) пройдет через передний главный фокус $F$ линзы (тот, что находится с той же стороны от линзы, что и источник $S$).
3. Точка $S'$, в которой пересекаются первый луч (прошедший через оптический центр) и продолжение второго преломленного луча, и является искомым изображением источника $S$. Так как изображение образовано пересечением не самих лучей, а их продолжений, оно является мнимым.
Графическое построение показано на рисунке ниже.
Ответ:
Построение изображения $S'$ точечного источника света $S$ показано на рисунке. Изображение является мнимым (получено на пересечении продолжений лучей), прямым (неперевернутым относительно главной оптической оси) и уменьшенным. Оно расположено с той же стороны от линзы, что и сам источник, между фокусом $F$ и оптическим центром $O$.
Другие задания:
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