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Номер 5, страница 150 - гдз по физике 9 класс учебник Изергин
Авторы: Изергин Э. Т.
Тип: Учебник
Серия: инновационная школа
Издательство: Русское слово
Год издания: 2019 - 2026
Цвет обложки: синий
ISBN: 978-5-533-01069-6
Популярные ГДЗ в 9 классе
Глава IV. Электромагнитные колебания и волны. § 31*. Дифракция света - номер 5, страница 150.
App\Models\Task {#1024 // 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" => 1439862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1439571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "IV" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #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" => "115" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 4169 "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 {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ 0 => App\Models\Term {#1048 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1049 #items: array:1 [ 0 => App\Models\Term {#1050 …30} ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" "alt" => "" "width" => "1881" "height" => "2502" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 …30} ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 4169 "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 {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043} "field_country" => Illuminate\Database\Eloquent\Collection {#1045} "field_city" => Illuminate\Database\Eloquent\Collection {#1047} "field_series" => Illuminate\Database\Eloquent\Collection {#1049} "field_umk" => Illuminate\Database\Eloquent\Collection {#1051} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1053} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1056} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" "alt" => "" "width" => "1881" "height" => "2502" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1057} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1059} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1060} "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 {#1062 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1439571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "IV" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "115" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1062} ] #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 {#1063 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1064 #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" => 1439580 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "§ 31*. Дифракция света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "147" "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 {#1066 #items: array:1 [ 0 => App\Models\Book {#1067 #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" => 4169 "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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 …30} ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1073 …30} ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1074 #items: array:1 [ 0 => App\Models\Term {#1075 …30} ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 …30} ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 …30} ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1081 #items: array:1 [ 0 => App\Models\Term {#1082 …30} ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Term {#1084 …30} ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1085 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Term {#1088 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1089 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" …3 ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1094 #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" => 4169 "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 {#1068} "field_class" => Illuminate\Database\Eloquent\Collection {#1070} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072} "field_author" => Illuminate\Database\Eloquent\Collection {#1074} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_country" => Illuminate\Database\Eloquent\Collection {#1079} "field_city" => Illuminate\Database\Eloquent\Collection {#1081} "field_series" => Illuminate\Database\Eloquent\Collection {#1083} "field_umk" => Illuminate\Database\Eloquent\Collection {#1085} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1086} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1087} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1089} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1090} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1091} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1092} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1093} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1094} "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 {#1096 #items: array:1 [ 0 => App\Models\Branch {#1097 #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" => 1439571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "IV" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "115" "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 {#1100 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1439571 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => "IV" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1098} "field_page_start" => "115" "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 {#1100} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1101} ] #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" => 1439580 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "§ 31*. Дифракция света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1065} "field_page_start" => "147" "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 {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1096} ] #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 {#1102 #items: array:2 [ 0 => App\Models\Element {#1103 #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" => 1707397 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Edition {#1105 #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" => 6139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1108 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6139 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1106} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1108} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1109} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1110} "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" => "1439862" "type" => "task" ] "text" => "<p><strong>5.</strong> При помощи дифракционной решётки с периодом 0,02 мм получены две фиолетовые линии с разных сторон от центральной линии на расстоянии 3,6 см от центральной линии и на расстоянии 1,8 м от решётки. Найдите длину световой волны.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1428" "height" => 373 "path" => "/media/fizika_09/izergin-u/0-31/5-1.webp?ts=1759529260" ] ] ] #original: array:7 [ "id" => 1707397 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104} "task" => array:2 [ "refs" => "1439862" "type" => "task" ] "text" => "<p><strong>5.</strong> При помощи дифракционной решётки с периодом 0,02 мм получены две фиолетовые линии с разных сторон от центральной линии на расстоянии 3,6 см от центральной линии и на расстоянии 1,8 м от решётки. Найдите длину световой волны.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1428" "height" => 373 "path" => "/media/fizika_09/izergin-u/0-31/5-1.webp?ts=1759529260" ] ] ] #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 {#1111 #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" => 1813415 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112 #items: array:1 [ 0 => App\Models\Edition {#1113 #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" => 6646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6646 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1114} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1116} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1117} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1118} "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" => "1439862" "type" => "task" ] "text" => "<p><strong>Дано</strong></p><p>Период дифракционной решётки, $d = 0,02 \text{ мм} = 0,02 \cdot 10^{-3} \text{ м} = 2 \cdot 10^{-5} \text{ м}$</p><p>Расстояние от решётки до экрана, $L = 1,8 \text{ м}$</p><p>Расстояние от центрального максимума до фиолетовой линии на экране, $x = 3,6 \text{ см} = 3,6 \cdot 10^{-2} \text{ м} = 0,036 \text{ м}$</p><p>Порядок дифракционного максимума, $k = 1$ (так как это ближайшие к центру линии)</p><p><strong>Найти:</strong></p><p>Длину световой волны, $\lambda$</p><p><strong>Решение</strong></p><p>Условие для наблюдения максимумов в дифракционной картине, полученной с помощью решётки, описывается формулой:</p><p>$d \sin\varphi = k\lambda$</p><p>где $\text{d}$ — период решётки, $\varphi$ — угол, под которым наблюдается максимум, $\text{k}$ — порядок максимума, $\lambda$ — длина волны света.</p><p>Угол $\varphi$ можно найти из геометрии установки. Рассмотрим прямоугольный треугольник, образованный направлением на центральный максимум (катет $\text{L}$), направлением на максимум первого порядка и отрезком на экране, соединяющим центральный и первый максимумы (катет $\text{x}$). Для этого треугольника справедливо соотношение:</p><p>$\tan\varphi = \frac{x}{L}$</p><p>В большинстве экспериментов с дифракционными решётками угол $\varphi$ достаточно мал. В этом случае можно использовать приближение $\sin\varphi \approx \tan\varphi$. Проверим, выполняется ли это условие:</p><p>$\tan\varphi = \frac{0,036 \text{ м}}{1,8 \text{ м}} = 0,02$</p><p>Значение тангенса мало, следовательно, угол мал, и приближение справедливо. Тогда можно записать:</p><p>$\sin\varphi \approx \frac{x}{L}$</p><p>Подставим это выражение в формулу дифракционной решётки:</p><p>$d \frac{x}{L} = k\lambda$</p><p>Выразим из этой формулы искомую длину волны $\lambda$:</p><p>$\lambda = \frac{d x}{k L}$</p><p>Подставим числовые значения и произведём вычисления, учитывая, что речь идёт о линиях первого порядка ($k=1$):</p><p>$\lambda = \frac{2 \cdot 10^{-5} \text{ м} \cdot 0,036 \text{ м}}{1 \cdot 1,8 \text{ м}} = \frac{0,072 \cdot 10^{-5} \text{ м}^2}{1,8 \text{ м}} = 0,04 \cdot 10^{-5} \text{ м} = 4 \cdot 10^{-7} \text{ м}$</p><p>Переведём результат в нанометры ($1 \text{ нм} = 10^{-9} \text{ м}$):</p><p>$4 \cdot 10^{-7} \text{ м} = 400 \cdot 10^{-9} \text{ м} = 400 \text{ нм}$</p><p>Полученное значение соответствует длине волны фиолетового света.</p><p><strong>Ответ:</strong> $\lambda = 400 \text{ нм}$.</p>" ] #original: array:6 [ "id" => 1813415 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1112} "task" => array:2 [ "refs" => "1439862" "type" => "task" ] "text" => "<p><strong>Дано</strong></p><p>Период дифракционной решётки, $d = 0,02 \text{ мм} = 0,02 \cdot 10^{-3} \text{ м} = 2 \cdot 10^{-5} \text{ м}$</p><p>Расстояние от решётки до экрана, $L = 1,8 \text{ м}$</p><p>Расстояние от центрального максимума до фиолетовой линии на экране, $x = 3,6 \text{ см} = 3,6 \cdot 10^{-2} \text{ м} = 0,036 \text{ м}$</p><p>Порядок дифракционного максимума, $k = 1$ (так как это ближайшие к центру линии)</p><p><strong>Найти:</strong></p><p>Длину световой волны, $\lambda$</p><p><strong>Решение</strong></p><p>Условие для наблюдения максимумов в дифракционной картине, полученной с помощью решётки, описывается формулой:</p><p>$d \sin\varphi = k\lambda$</p><p>где $\text{d}$ — период решётки, $\varphi$ — угол, под которым наблюдается максимум, $\text{k}$ — порядок максимума, $\lambda$ — длина волны света.</p><p>Угол $\varphi$ можно найти из геометрии установки. Рассмотрим прямоугольный треугольник, образованный направлением на центральный максимум (катет $\text{L}$), направлением на максимум первого порядка и отрезком на экране, соединяющим центральный и первый максимумы (катет $\text{x}$). Для этого треугольника справедливо соотношение:</p><p>$\tan\varphi = \frac{x}{L}$</p><p>В большинстве экспериментов с дифракционными решётками угол $\varphi$ достаточно мал. В этом случае можно использовать приближение $\sin\varphi \approx \tan\varphi$. Проверим, выполняется ли это условие:</p><p>$\tan\varphi = \frac{0,036 \text{ м}}{1,8 \text{ м}} = 0,02$</p><p>Значение тангенса мало, следовательно, угол мал, и приближение справедливо. Тогда можно записать:</p><p>$\sin\varphi \approx \frac{x}{L}$</p><p>Подставим это выражение в формулу дифракционной решётки:</p><p>$d \frac{x}{L} = k\lambda$</p><p>Выразим из этой формулы искомую длину волны $\lambda$:</p><p>$\lambda = \frac{d x}{k L}$</p><p>Подставим числовые значения и произведём вычисления, учитывая, что речь идёт о линиях первого порядка ($k=1$):</p><p>$\lambda = \frac{2 \cdot 10^{-5} \text{ м} \cdot 0,036 \text{ м}}{1 \cdot 1,8 \text{ м}} = \frac{0,072 \cdot 10^{-5} \text{ м}^2}{1,8 \text{ м}} = 0,04 \cdot 10^{-5} \text{ м} = 4 \cdot 10^{-7} \text{ м}$</p><p>Переведём результат в нанометры ($1 \text{ нм} = 10^{-9} \text{ м}$):</p><p>$4 \cdot 10^{-7} \text{ м} = 400 \cdot 10^{-9} \text{ м} = 400 \text{ нм}$</p><p>Полученное значение соответствует длине волны фиолетового света.</p><p><strong>Ответ:</strong> $\lambda = 400 \text{ нм}$.</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" => "1439863" "type" => "task" ] "previous" => array:2 [ "refs" => "1439861" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1119 #items: array:1 [ 0 => App\Models\Book {#1120 #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" => 4169 "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 {#1121 #items: array:1 [ 0 => App\Models\Term {#1122 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #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 {#1123 #items: array:1 [ 0 => App\Models\Term {#1124 #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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "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 {#1125 #items: array:1 [ 0 => App\Models\Term {#1126 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5176 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Русское слово" "field_cases" => null "field_translit" => "russkoe slovo" ] #original: array:6 [ "id" => 5176 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Русское слово" "field_cases" => null "field_translit" => "russkoe slovo" ] #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 {#1127 #items: array:1 [ 0 => App\Models\Term {#1128 #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" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1136 #items: array:1 [ 0 => App\Models\Term {#1137 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4715 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "инновационная школа" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "innovacionnaya shkola" ] #original: array:8 [ "id" => 4715 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "инновационная школа" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "innovacionnaya shkola" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1138 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1143 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" "alt" => "" "width" => "1881" "height" => "2502" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1144 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ 0 => App\Models\Term {#1148 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #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" => 4169 "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 {#1121} "field_class" => Illuminate\Database\Eloquent\Collection {#1123} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1125} "field_author" => Illuminate\Database\Eloquent\Collection {#1127} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1138} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1139} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1143} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" "alt" => "" "width" => "1881" "height" => "2502" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1144} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1145} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1147} "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 } "page" => Illuminate\Database\Eloquent\Collection {#1335 #items: array:1 [ 0 => App\Models\BookPage {#1153 #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" => 1439468 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_url" => "/9-klass/fizika/izergin-uchebnik/page-150" "field_display_title" => "150" "field_folder" => "1" "field_image_name" => "150" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1156 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Book {#1157 #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" => 4169 "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 {#1158 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1166 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1167 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1169 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1175 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1176 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1179 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1180 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1181 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1182 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1183 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1184 #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" => 4169 "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 {#1158} "field_class" => Illuminate\Database\Eloquent\Collection {#1160} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1162} "field_author" => Illuminate\Database\Eloquent\Collection {#1164} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1166} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1167} "field_country" => Illuminate\Database\Eloquent\Collection {#1169} "field_city" => Illuminate\Database\Eloquent\Collection {#1171} "field_series" => Illuminate\Database\Eloquent\Collection {#1173} "field_umk" => Illuminate\Database\Eloquent\Collection {#1175} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1176} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1177} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1179} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1180} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 9 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "388" "field_priority" => null "field_default_folder" => "/fizika_09/izergin-u/" "field_isbn" => "978-5-533-01069-6" "field_cover" => array:1 [ 0 => "/media/fizika_09/izergin-u/covers/cover1.webp?ts=1759162386" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1181} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1182} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1183} "field_url" => "/9-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1184} "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 } "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 {#1186 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1187 #items: array:1 [ 0 => App\Models\Element {#1188 #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" => 1707706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1189 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1707706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1189} "book_page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #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" => "1439469" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1439467" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:3 [ 0 => App\Models\Task {#1197 #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" => 1439861 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198 #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 "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1200 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1201 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1275 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1439862" "type" => "task" ] "previous" => array:2 [ "refs" => "1439860" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1292 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] ] #original: array:24 [ "id" => 1439861 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198} "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 {#1200} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1201} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1236} "content" => Illuminate\Database\Eloquent\Collection {#1275} "next" => array:2 [ "refs" => "1439862" "type" => "task" ] "previous" => array:2 [ "refs" => "1439860" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1292} "page" => array:2 [ "refs" => "1439468" "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 => "*" ] } 1 => App\Models\Task {#1293 #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" => 1439862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 #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 "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1295 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1298 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1439863" "type" => "task" ] "previous" => array:2 [ "refs" => "1439861" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1315 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] ] #original: array:24 [ "id" => 1439862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294} "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 {#1295} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297} "content" => Illuminate\Database\Eloquent\Collection {#1298} "next" => array:2 [ "refs" => "1439863" "type" => "task" ] "previous" => array:2 [ "refs" => "1439861" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1315} "page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1316 #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" => 1439863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => "151" "field_url" => "/9-klass/fizika/izergin-uchebnik/labrab-5" "field_display_title" => "Лабораторная работа 5" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317 #items: [] #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 {#1318 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1319 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320 #items: array:2 [ …2] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1321 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1439864" "type" => "task" ] "previous" => array:2 [ "refs" => "1439862" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1332 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1439468" "type" => "book_page" ] ] #original: array:24 [ "id" => 1439863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => "151" "field_url" => "/9-klass/fizika/izergin-uchebnik/labrab-5" "field_display_title" => "Лабораторная работа 5" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1317} "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 {#1318} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1319} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1320} "content" => Illuminate\Database\Eloquent\Collection {#1321} "next" => array:2 [ "refs" => "1439864" "type" => "task" ] "previous" => array:2 [ "refs" => "1439862" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1332} "page" => array:2 [ "refs" => "1439468" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1439468 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_url" => "/9-klass/fizika/izergin-uchebnik/page-150" "field_display_title" => "150" "field_folder" => "1" "field_image_name" => "150" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1156} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1155} "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 {#1186} "content" => Illuminate\Database\Eloquent\Collection {#1187} "next" => array:2 [ "refs" => "1439469" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1439467" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1196} ] #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" => 1439862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "150" "field_page_end" => null "field_url" => "/9-klass/fizika/izergin-uchebnik/31-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "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 {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1063} "content" => Illuminate\Database\Eloquent\Collection {#1102} "next" => array:2 [ "refs" => "1439863" "type" => "task" ] "previous" => array:2 [ "refs" => "1439861" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1119} "page" => array:2 [ "refs" => "1439468" "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. 150)
Условие. №5 (с. 150)
скриншот условия
5. При помощи дифракционной решётки с периодом 0,02 мм получены две фиолетовые линии с разных сторон от центральной линии на расстоянии 3,6 см от центральной линии и на расстоянии 1,8 м от решётки. Найдите длину световой волны.
Решение. №5 (с. 150)
Дано
Период дифракционной решётки, $d = 0,02 \text{ мм} = 0,02 \cdot 10^{-3} \text{ м} = 2 \cdot 10^{-5} \text{ м}$
Расстояние от решётки до экрана, $L = 1,8 \text{ м}$
Расстояние от центрального максимума до фиолетовой линии на экране, $x = 3,6 \text{ см} = 3,6 \cdot 10^{-2} \text{ м} = 0,036 \text{ м}$
Порядок дифракционного максимума, $k = 1$ (так как это ближайшие к центру линии)
Найти:
Длину световой волны, $\lambda$
Решение
Условие для наблюдения максимумов в дифракционной картине, полученной с помощью решётки, описывается формулой:
$d \sin\varphi = k\lambda$
где $\text{d}$ — период решётки, $\varphi$ — угол, под которым наблюдается максимум, $\text{k}$ — порядок максимума, $\lambda$ — длина волны света.
Угол $\varphi$ можно найти из геометрии установки. Рассмотрим прямоугольный треугольник, образованный направлением на центральный максимум (катет $\text{L}$), направлением на максимум первого порядка и отрезком на экране, соединяющим центральный и первый максимумы (катет $\text{x}$). Для этого треугольника справедливо соотношение:
$\tan\varphi = \frac{x}{L}$
В большинстве экспериментов с дифракционными решётками угол $\varphi$ достаточно мал. В этом случае можно использовать приближение $\sin\varphi \approx \tan\varphi$. Проверим, выполняется ли это условие:
$\tan\varphi = \frac{0,036 \text{ м}}{1,8 \text{ м}} = 0,02$
Значение тангенса мало, следовательно, угол мал, и приближение справедливо. Тогда можно записать:
$\sin\varphi \approx \frac{x}{L}$
Подставим это выражение в формулу дифракционной решётки:
$d \frac{x}{L} = k\lambda$
Выразим из этой формулы искомую длину волны $\lambda$:
$\lambda = \frac{d x}{k L}$
Подставим числовые значения и произведём вычисления, учитывая, что речь идёт о линиях первого порядка ($k=1$):
$\lambda = \frac{2 \cdot 10^{-5} \text{ м} \cdot 0,036 \text{ м}}{1 \cdot 1,8 \text{ м}} = \frac{0,072 \cdot 10^{-5} \text{ м}^2}{1,8 \text{ м}} = 0,04 \cdot 10^{-5} \text{ м} = 4 \cdot 10^{-7} \text{ м}$
Переведём результат в нанометры ($1 \text{ нм} = 10^{-9} \text{ м}$):
$4 \cdot 10^{-7} \text{ м} = 400 \cdot 10^{-9} \text{ м} = 400 \text{ нм}$
Полученное значение соответствует длине волны фиолетового света.
Ответ: $\lambda = 400 \text{ нм}$.
Другие задания:
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