gdz.top
Номер 35.5, страница 248 - гдз по физике 10-11 класс задачник Гельфгат, Генденштейн
Авторы: Гельфгат И. М., Генденштейн Л. Э., Кирик Л. А.
Тип: Задачник
Издательство: Илекса
Год издания: 2008 - 2026
Уровень обучения: профильный
Цвет обложки: красный лупа, парень едет на велосипеде
ISBN: 978-5-89237-252-7
Популярные ГДЗ в 10 классе
Электродинамика. Электромагнитные колебания и волны. 35. Волновые свойства света. Упражнения - номер 35.5, страница 248.
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" => 1319796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "248" "field_page_end" => "249" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/35-5" "field_display_title" => "35.5" "field_outside_task" => "0" "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 {#1074 #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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ 0 => App\Models\Book {#1040 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5400 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1071 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "163" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1038} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #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 {#1268 #items: array:4 [ 0 => App\Models\Branch {#1072 #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" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "163" "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 {#1073 #items: array:1 [ 0 => App\Models\Book {#1076 #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" => 5400 "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 {#1077 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5400 "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 {#1077 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1082 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1095 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1100 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1104 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1107 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1075} "field_page_start" => "163" "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 {#1073} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1107} ] #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 {#1108 #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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "241" "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 {#1110 #items: array:1 [ 0 => App\Models\Book {#1111 #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" => 5400 "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 {#1112 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5400 "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 {#1112 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1114 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1119 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1123 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1124 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1126 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1128 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1142 #items: array:1 [ 0 => App\Models\Branch {#1143 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_page_start" => "163" "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 {#1145 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 …2} ] #original: array:24 [ "id" => 1319339 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электродинамика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_page_start" => "163" "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 {#1145 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1146 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1109} "field_page_start" => "241" "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 {#1110} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1142} ] #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 {#1147 #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" => 1319376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "35. Волновые свойства света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1148 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "247" "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 {#1149 #items: array:1 [ 0 => App\Models\Book {#1150 #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" => 5400 "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 {#1151 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1158 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5400 "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 {#1151 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1156 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1158 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1162 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1163 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1165 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1167 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1170 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1171 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1173 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1174 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1176 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1177 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1178 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1179 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1181 #items: array:1 [ 0 => App\Models\Branch {#1182 #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" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_page_start" => "241" "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 {#1184 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1185 …2} ] #original: array:24 [ "id" => 1319371 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Электромагнитные колебания и волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183 …2} "field_page_start" => "241" "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 {#1184 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1185 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "35. Волновые свойства света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1148} "field_page_start" => "247" "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 {#1149} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1181} ] #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\Branch {#1190 #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" => 1319377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1191 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "247" "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 {#1192 #items: array:1 [ 0 => App\Models\Book {#1193 #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" => 5400 "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 {#1194 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1196 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1217 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1220 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1222 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 5400 "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 {#1194 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1196 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1210 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1217 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1219 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1220 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1222 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #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 {#1224 #items: array:1 [ 0 => App\Models\Branch {#1225 #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" => 1319376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "35. Волновые свойства света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1226 …2} "field_page_start" => "247" "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 {#1227 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1228 …2} ] #original: array:24 [ "id" => 1319376 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "35. Волновые свойства света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1226 …2} "field_page_start" => "247" "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 {#1227 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1228 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319377 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1191} "field_page_start" => "247" "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 {#1192} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1224} ] #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 {#1279 #items: array:2 [ 0 => App\Models\Element {#1287 #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" => 1493944 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1296 #items: array:1 [ 0 => App\Models\Edition {#1288 #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" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1290 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1291 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1292 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1293 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5430 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1290 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1291 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1292 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1293 …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" => "1319796" "type" => "task" ] "text" => "<p><strong>35.5.</strong> Два когерентных источника монохроматического света с длиной волны $\lambda = 600$ нм находятся на расстоянии $A_1A_2 = 1$ мм друг от друга и на одинаковом расстоянии $L = 3$ м от экрана (см. схематический рисунок). Каково расстояние $\text{x}$ между ближайшими максимумами освещенности (серединами светлых полос) на экране? Будет ли наблюдаться максимум освещенности в точке $\text{O}$, равноудаленной от обоих источников?</p><p>☑ $x = 1,8$ мм; не обязательно.</p><p><strong><em>Решение.</em></strong> Когерентность источников не исключает возможности постоянного сдвига фаз между испускаемыми ими волнами. Поэтому в равноудаленной от источников точке $\text{O}$ не обязательно будет максимум освещенности: например, в случае противофазных источников в точке $\text{O}$ будет минимум освещенности. Для нахождения $\text{x}$ предположим, что сдвиг фаз между источниками отсутствует (в противном случае произойдет одинаковое смещение темных и светлых полос без изменения их ширины). Тогда в точке $\text{O}$ будет максимум освещенности, поскольку разность хода волн равна нулю, а в точке $\text{M}$ следующего максимума (см. рисунок) разность хода волн равна длине волны $\lambda$. Это условие приводит к уравнению $\sqrt{L^2 + (x + s)^2} - \sqrt{L^2 + (x - s)^2} = \lambda$, где $s = A_1A_2/2$.</p><p>Воспользовавшись малостью $\text{x}$ и $\text{s}$ по сравнению с $\text{L}$, можно упростить последнее уравнение. Домножив и разделив его левую часть на «сопряженное» выражение $\sqrt{L^2 + (x + s)^2} + \sqrt{L^2 + (x - s)^2}$, приближенно равное $2L$, находим $x = \frac{\lambda L}{2s} = \frac{\lambda L}{A_1A_2} = 1,8$ (мм). Для упрощения уравнения можно также использовать применимую при $x \ll 1$ формулу $\sqrt{1 + x} \approx 1 + x/2$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1401" "height" => 897 "path" => "/media/fizika_10/gelfgat-z/0-35/5-1.webp?ts=1756251143" ] 1 => array:5 [ "name" => "5-2.jpg" "alt" => null "width" => "1364" "height" => 1949 "path" => "/media/fizika_10/gelfgat-z/0-35/5-2.webp?ts=1756251143" ] ] ] #original: array:7 [ "id" => 1493944 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1296} "task" => array:2 [ "refs" => "1319796" "type" => "task" ] "text" => "<p><strong>35.5.</strong> Два когерентных источника монохроматического света с длиной волны $\lambda = 600$ нм находятся на расстоянии $A_1A_2 = 1$ мм друг от друга и на одинаковом расстоянии $L = 3$ м от экрана (см. схематический рисунок). Каково расстояние $\text{x}$ между ближайшими максимумами освещенности (серединами светлых полос) на экране? Будет ли наблюдаться максимум освещенности в точке $\text{O}$, равноудаленной от обоих источников?</p><p>☑ $x = 1,8$ мм; не обязательно.</p><p><strong><em>Решение.</em></strong> Когерентность источников не исключает возможности постоянного сдвига фаз между испускаемыми ими волнами. Поэтому в равноудаленной от источников точке $\text{O}$ не обязательно будет максимум освещенности: например, в случае противофазных источников в точке $\text{O}$ будет минимум освещенности. Для нахождения $\text{x}$ предположим, что сдвиг фаз между источниками отсутствует (в противном случае произойдет одинаковое смещение темных и светлых полос без изменения их ширины). Тогда в точке $\text{O}$ будет максимум освещенности, поскольку разность хода волн равна нулю, а в точке $\text{M}$ следующего максимума (см. рисунок) разность хода волн равна длине волны $\lambda$. Это условие приводит к уравнению $\sqrt{L^2 + (x + s)^2} - \sqrt{L^2 + (x - s)^2} = \lambda$, где $s = A_1A_2/2$.</p><p>Воспользовавшись малостью $\text{x}$ и $\text{s}$ по сравнению с $\text{L}$, можно упростить последнее уравнение. Домножив и разделив его левую часть на «сопряженное» выражение $\sqrt{L^2 + (x + s)^2} + \sqrt{L^2 + (x - s)^2}$, приближенно равное $2L$, находим $x = \frac{\lambda L}{2s} = \frac{\lambda L}{A_1A_2} = 1,8$ (мм). Для упрощения уравнения можно также использовать применимую при $x \ll 1$ формулу $\sqrt{1 + x} \approx 1 + x/2$.</p>" "img" => array:2 [ 0 => array:5 [ "name" => "5-1.jpg" "alt" => null "width" => "1401" "height" => 897 "path" => "/media/fizika_10/gelfgat-z/0-35/5-1.webp?ts=1756251143" ] 1 => array:5 [ "name" => "5-2.jpg" "alt" => null "width" => "1364" "height" => 1949 "path" => "/media/fizika_10/gelfgat-z/0-35/5-2.webp?ts=1756251143" ] ] ] #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 {#1294 #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" => 1691501 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1304 #items: array:1 [ 0 => App\Models\Edition {#1295 #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" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1298 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1299 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1300 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1301 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6138 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1298 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" …9 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1319796" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина волны монохроматического света, $ \lambda = 600 \text{ нм} $</p><p>Расстояние между когерентными источниками, $ d = A_1A_2 = 1 \text{ мм} $</p><p>Расстояние от источников до экрана, $ L = 3 \text{ м} $</p><p>Перевод в систему СИ:</p><p>$ \lambda = 600 \cdot 10^{-9} \text{ м} $</p><p>$ d = 1 \cdot 10^{-3} \text{ м} $</p><p>$ L = 3 \text{ м} $</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Расстояние $ x $ между ближайшими максимумами освещенности.</p><p><strong>2.</strong> Будет ли наблюдаться максимум освещенности в точке O.</p><p><strong>Решение:</strong></p><p><strong>Каково расстояние x между ближайшими максимумами освещенности (серединами светлых полос) на экране?</strong></p><p>Интерференционная картина, наблюдаемая на экране, представляет собой чередование светлых и темных полос. Светлые полосы (максимумы освещенности) возникают в тех точках экрана, где разность хода лучей от двух источников $ \Delta r $ равна целому числу длин волн:</p><p>$ \Delta r = k \lambda $, где $ k = 0, \pm 1, \pm 2, ... $</p><p>Рассмотрим точку на экране, находящуюся на расстоянии $ x_k $ от центральной точки O. Поскольку расстояние от источников до экрана $ L $ значительно больше расстояния между источниками $ d $ и расстояния $ x_k $ до рассматриваемой точки ($L \gg d$ и $L \gg x_k$), разность хода $ \Delta r $ можно вычислить по приближенной формуле:</p><p>$ \Delta r \approx \frac{d \cdot x_k}{L} $</p><p>Приравнивая два выражения для разности хода, получаем условие для положения $ k $-го максимума:</p><p>$ \frac{d \cdot x_k}{L} = k \lambda $</p><p>Отсюда координата $ k $-го максимума:</p><p>$ x_k = \frac{k \lambda L}{d} $</p><p>Расстояние $ x $ между двумя соседними максимумами (например, для $ k $ и $ k+1 $) является постоянной величиной и называется шириной интерференционной полосы.</p><p>$ x = x_{k+1} - x_k = \frac{(k+1) \lambda L}{d} - \frac{k \lambda L}{d} = \frac{\lambda L}{d} $</p><p>Подставим числовые значения:</p><p>$ x = \frac{600 \cdot 10^{-9} \text{ м} \cdot 3 \text{ м}}{1 \cdot 10^{-3} \text{ м}} = \frac{1800 \cdot 10^{-9}}{10^{-3}} \text{ м} = 1800 \cdot 10^{-6} \text{ м} = 1.8 \cdot 10^{-3} \text{ м} = 1.8 \text{ мм} $</p><p><strong>Ответ:</strong> Расстояние между ближайшими максимумами освещенности составляет $ 1.8 \text{ мм} $.</p><p><strong>Будет ли наблюдаться максимум освещенности в точке O, равноудаленной от обоих источников?</strong></p><p>Точка O на экране равноудалена от источников $ A_1 $ и $ A_2 $. Это означает, что оптическая разность хода лучей, приходящих в эту точку, равна нулю ($ \Delta r = 0 $).</p><p>Результат интерференции в точке O зависит от полной разности фаз $ \Delta \varphi $ колебаний, приходящих в эту точку. Полная разность фаз складывается из разности фаз, вызванной разностью хода, и начальной разности фаз источников $ \Delta \varphi_0 $:</p><p>$ \Delta \varphi = \frac{2\pi}{\lambda} \Delta r + \Delta \varphi_0 $</p><p>Поскольку в точке O разность хода $ \Delta r = 0 $, то полная разность фаз равна начальной разности фаз источников: $ \Delta \varphi = \Delta \varphi_0 $.</p><p>Условием максимума интерференции является кратность полной разности фаз $ 2\pi $: $ \Delta \varphi = 2\pi k $, где $ k $ — целое число.</p><p>В условии задачи сказано, что источники когерентны. Когерентность означает, что начальная разность фаз $ \Delta \varphi_0 $ постоянна во времени, но не обязательно равна нулю. Если источники синфазны (колебания происходят в одинаковой фазе), то $ \Delta \varphi_0 = 0 $, и в точке O будет наблюдаться главный максимум освещенности. Однако если источники находятся в противофазе (сдвиг фаз равен $ \pi $), то $ \Delta \varphi_0 = \pi $, и в точке O будет наблюдаться минимум освещенности. Так как в условии задачи не указана начальная разность фаз источников, однозначно утверждать, что в точке O будет максимум, нельзя.</p><p><strong>Ответ:</strong> Не обязательно. Максимум в точке O будет наблюдаться только в том случае, если источники являются синфазными (начальная разность фаз равна нулю). Если источники находятся в противофазе, в точке O будет наблюдаться минимум.</p>" ] #original: array:6 [ "id" => 1691501 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1304} "task" => array:2 [ "refs" => "1319796" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина волны монохроматического света, $ \lambda = 600 \text{ нм} $</p><p>Расстояние между когерентными источниками, $ d = A_1A_2 = 1 \text{ мм} $</p><p>Расстояние от источников до экрана, $ L = 3 \text{ м} $</p><p>Перевод в систему СИ:</p><p>$ \lambda = 600 \cdot 10^{-9} \text{ м} $</p><p>$ d = 1 \cdot 10^{-3} \text{ м} $</p><p>$ L = 3 \text{ м} $</p><p><strong>Найти:</strong></p><p><strong>1.</strong> Расстояние $ x $ между ближайшими максимумами освещенности.</p><p><strong>2.</strong> Будет ли наблюдаться максимум освещенности в точке O.</p><p><strong>Решение:</strong></p><p><strong>Каково расстояние x между ближайшими максимумами освещенности (серединами светлых полос) на экране?</strong></p><p>Интерференционная картина, наблюдаемая на экране, представляет собой чередование светлых и темных полос. Светлые полосы (максимумы освещенности) возникают в тех точках экрана, где разность хода лучей от двух источников $ \Delta r $ равна целому числу длин волн:</p><p>$ \Delta r = k \lambda $, где $ k = 0, \pm 1, \pm 2, ... $</p><p>Рассмотрим точку на экране, находящуюся на расстоянии $ x_k $ от центральной точки O. Поскольку расстояние от источников до экрана $ L $ значительно больше расстояния между источниками $ d $ и расстояния $ x_k $ до рассматриваемой точки ($L \gg d$ и $L \gg x_k$), разность хода $ \Delta r $ можно вычислить по приближенной формуле:</p><p>$ \Delta r \approx \frac{d \cdot x_k}{L} $</p><p>Приравнивая два выражения для разности хода, получаем условие для положения $ k $-го максимума:</p><p>$ \frac{d \cdot x_k}{L} = k \lambda $</p><p>Отсюда координата $ k $-го максимума:</p><p>$ x_k = \frac{k \lambda L}{d} $</p><p>Расстояние $ x $ между двумя соседними максимумами (например, для $ k $ и $ k+1 $) является постоянной величиной и называется шириной интерференционной полосы.</p><p>$ x = x_{k+1} - x_k = \frac{(k+1) \lambda L}{d} - \frac{k \lambda L}{d} = \frac{\lambda L}{d} $</p><p>Подставим числовые значения:</p><p>$ x = \frac{600 \cdot 10^{-9} \text{ м} \cdot 3 \text{ м}}{1 \cdot 10^{-3} \text{ м}} = \frac{1800 \cdot 10^{-9}}{10^{-3}} \text{ м} = 1800 \cdot 10^{-6} \text{ м} = 1.8 \cdot 10^{-3} \text{ м} = 1.8 \text{ мм} $</p><p><strong>Ответ:</strong> Расстояние между ближайшими максимумами освещенности составляет $ 1.8 \text{ мм} $.</p><p><strong>Будет ли наблюдаться максимум освещенности в точке O, равноудаленной от обоих источников?</strong></p><p>Точка O на экране равноудалена от источников $ A_1 $ и $ A_2 $. Это означает, что оптическая разность хода лучей, приходящих в эту точку, равна нулю ($ \Delta r = 0 $).</p><p>Результат интерференции в точке O зависит от полной разности фаз $ \Delta \varphi $ колебаний, приходящих в эту точку. Полная разность фаз складывается из разности фаз, вызванной разностью хода, и начальной разности фаз источников $ \Delta \varphi_0 $:</p><p>$ \Delta \varphi = \frac{2\pi}{\lambda} \Delta r + \Delta \varphi_0 $</p><p>Поскольку в точке O разность хода $ \Delta r = 0 $, то полная разность фаз равна начальной разности фаз источников: $ \Delta \varphi = \Delta \varphi_0 $.</p><p>Условием максимума интерференции является кратность полной разности фаз $ 2\pi $: $ \Delta \varphi = 2\pi k $, где $ k $ — целое число.</p><p>В условии задачи сказано, что источники когерентны. Когерентность означает, что начальная разность фаз $ \Delta \varphi_0 $ постоянна во времени, но не обязательно равна нулю. Если источники синфазны (колебания происходят в одинаковой фазе), то $ \Delta \varphi_0 = 0 $, и в точке O будет наблюдаться главный максимум освещенности. Однако если источники находятся в противофазе (сдвиг фаз равен $ \pi $), то $ \Delta \varphi_0 = \pi $, и в точке O будет наблюдаться минимум освещенности. Так как в условии задачи не указана начальная разность фаз источников, однозначно утверждать, что в точке O будет максимум, нельзя.</p><p><strong>Ответ:</strong> Не обязательно. Максимум в точке O будет наблюдаться только в том случае, если источники являются синфазными (начальная разность фаз равна нулю). Если источники находятся в противофазе, в точке O будет наблюдаться минимум.</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" => "1319797" "type" => "task" ] "previous" => array:2 [ "refs" => "1319795" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1320 #items: array:1 [ 0 => App\Models\Book {#1284 #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" => 5400 "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 {#1271 #items: array:1 [ 0 => App\Models\Term {#1270 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:2 [ 0 => App\Models\Term {#1276 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1275 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:1 [ 0 => App\Models\Term {#1272 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1273 #items: array:3 [ 0 => App\Models\Term {#1278 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Term {#1277 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Term {#1286 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1282 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1280 #items: array:1 [ 0 => App\Models\Term {#1283 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1281 #items: array:1 [ 0 => App\Models\Term {#1302 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1303 #items: array:1 [ 0 => App\Models\Term {#1305 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1306 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1307 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1308 #items: array:1 [ 0 => App\Models\Term {#1309 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1310 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1311 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1312 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1313 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1314 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1315 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1316 #items: array:1 [ 0 => App\Models\Term {#1317 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #original: array:50 [ "id" => 5400 "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 {#1271} "field_class" => Illuminate\Database\Eloquent\Collection {#1269} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1274} "field_author" => Illuminate\Database\Eloquent\Collection {#1273} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1282} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1280} "field_country" => Illuminate\Database\Eloquent\Collection {#1281} "field_city" => Illuminate\Database\Eloquent\Collection {#1303} "field_series" => Illuminate\Database\Eloquent\Collection {#1306} "field_umk" => Illuminate\Database\Eloquent\Collection {#1307} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1308} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1310} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1311} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1312} "field_under_the_edition_degree" => null "field_cover_description" => "лупа, парень едет на велосипеде" "field_publication_year" => "2008" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "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" => "459" "field_priority" => null "field_default_folder" => "/fizika_10/gelfgat-z/" "field_isbn" => "978-5-89237-252-7" "field_cover" => array:1 [ 0 => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/gelfgat-z/covers/cover1.webp?ts=1756049816" "alt" => "" "width" => "1566" "height" => "2412" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1313} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1314} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1315} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1316} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 381 "subject" => 556 "class_subject" => 494 ] ] #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 {#1325 #items: array:1 [ 0 => App\Models\BookPage {#1324 #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" => 1341209 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "248" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-248" "field_display_title" => "248" "field_folder" => "1" "field_image_name" => "248" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1326 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1327 #items: array:1 [ 0 => App\Models\Book {#1284} ] #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 {#1328 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1338 #items: array:1 [ 0 => App\Models\Element {#1337 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1341210" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341208" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1619 #items: array:3 [ 0 => App\Models\Task {#1629 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => App\Models\Task {#1634 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 2 => App\Models\Task {#1638 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341209 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "248" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-248" "field_display_title" => "248" "field_folder" => "1" "field_image_name" => "248" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1326} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1327} "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 {#1328} "content" => Illuminate\Database\Eloquent\Collection {#1338} "next" => array:2 [ "refs" => "1341210" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341208" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1619} ] #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" => 1319796 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "248" "field_page_end" => "249" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/35-5" "field_display_title" => "35.5" "field_outside_task" => "0" "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 {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1268} "content" => Illuminate\Database\Eloquent\Collection {#1279} "next" => array:2 [ "refs" => "1319797" "type" => "task" ] "previous" => array:2 [ "refs" => "1319795" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1320} "page" => array:2 [ "refs" => "1341209" "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 => "*" ] }
№35.5 (с. 248)
Условие. №35.5 (с. 248)
скриншот условия
35.5. Два когерентных источника монохроматического света с длиной волны $\lambda = 600$ нм находятся на расстоянии $A_1A_2 = 1$ мм друг от друга и на одинаковом расстоянии $L = 3$ м от экрана (см. схематический рисунок). Каково расстояние $\text{x}$ между ближайшими максимумами освещенности (серединами светлых полос) на экране? Будет ли наблюдаться максимум освещенности в точке $\text{O}$, равноудаленной от обоих источников?
☑ $x = 1,8$ мм; не обязательно.
Решение. Когерентность источников не исключает возможности постоянного сдвига фаз между испускаемыми ими волнами. Поэтому в равноудаленной от источников точке $\text{O}$ не обязательно будет максимум освещенности: например, в случае противофазных источников в точке $\text{O}$ будет минимум освещенности. Для нахождения $\text{x}$ предположим, что сдвиг фаз между источниками отсутствует (в противном случае произойдет одинаковое смещение темных и светлых полос без изменения их ширины). Тогда в точке $\text{O}$ будет максимум освещенности, поскольку разность хода волн равна нулю, а в точке $\text{M}$ следующего максимума (см. рисунок) разность хода волн равна длине волны $\lambda$. Это условие приводит к уравнению $\sqrt{L^2 + (x + s)^2} - \sqrt{L^2 + (x - s)^2} = \lambda$, где $s = A_1A_2/2$.
Воспользовавшись малостью $\text{x}$ и $\text{s}$ по сравнению с $\text{L}$, можно упростить последнее уравнение. Домножив и разделив его левую часть на «сопряженное» выражение $\sqrt{L^2 + (x + s)^2} + \sqrt{L^2 + (x - s)^2}$, приближенно равное $2L$, находим $x = \frac{\lambda L}{2s} = \frac{\lambda L}{A_1A_2} = 1,8$ (мм). Для упрощения уравнения можно также использовать применимую при $x \ll 1$ формулу $\sqrt{1 + x} \approx 1 + x/2$.
Решение. №35.5 (с. 248)
Дано:
Длина волны монохроматического света, $ \lambda = 600 \text{ нм} $
Расстояние между когерентными источниками, $ d = A_1A_2 = 1 \text{ мм} $
Расстояние от источников до экрана, $ L = 3 \text{ м} $
Перевод в систему СИ:
$ \lambda = 600 \cdot 10^{-9} \text{ м} $
$ d = 1 \cdot 10^{-3} \text{ м} $
$ L = 3 \text{ м} $
Найти:
1. Расстояние $ x $ между ближайшими максимумами освещенности.
2. Будет ли наблюдаться максимум освещенности в точке O.
Решение:
Каково расстояние x между ближайшими максимумами освещенности (серединами светлых полос) на экране?
Интерференционная картина, наблюдаемая на экране, представляет собой чередование светлых и темных полос. Светлые полосы (максимумы освещенности) возникают в тех точках экрана, где разность хода лучей от двух источников $ \Delta r $ равна целому числу длин волн:
$ \Delta r = k \lambda $, где $ k = 0, \pm 1, \pm 2, ... $
Рассмотрим точку на экране, находящуюся на расстоянии $ x_k $ от центральной точки O. Поскольку расстояние от источников до экрана $ L $ значительно больше расстояния между источниками $ d $ и расстояния $ x_k $ до рассматриваемой точки ($L \gg d$ и $L \gg x_k$), разность хода $ \Delta r $ можно вычислить по приближенной формуле:
$ \Delta r \approx \frac{d \cdot x_k}{L} $
Приравнивая два выражения для разности хода, получаем условие для положения $ k $-го максимума:
$ \frac{d \cdot x_k}{L} = k \lambda $
Отсюда координата $ k $-го максимума:
$ x_k = \frac{k \lambda L}{d} $
Расстояние $ x $ между двумя соседними максимумами (например, для $ k $ и $ k+1 $) является постоянной величиной и называется шириной интерференционной полосы.
$ x = x_{k+1} - x_k = \frac{(k+1) \lambda L}{d} - \frac{k \lambda L}{d} = \frac{\lambda L}{d} $
Подставим числовые значения:
$ x = \frac{600 \cdot 10^{-9} \text{ м} \cdot 3 \text{ м}}{1 \cdot 10^{-3} \text{ м}} = \frac{1800 \cdot 10^{-9}}{10^{-3}} \text{ м} = 1800 \cdot 10^{-6} \text{ м} = 1.8 \cdot 10^{-3} \text{ м} = 1.8 \text{ мм} $
Ответ: Расстояние между ближайшими максимумами освещенности составляет $ 1.8 \text{ мм} $.
Будет ли наблюдаться максимум освещенности в точке O, равноудаленной от обоих источников?
Точка O на экране равноудалена от источников $ A_1 $ и $ A_2 $. Это означает, что оптическая разность хода лучей, приходящих в эту точку, равна нулю ($ \Delta r = 0 $).
Результат интерференции в точке O зависит от полной разности фаз $ \Delta \varphi $ колебаний, приходящих в эту точку. Полная разность фаз складывается из разности фаз, вызванной разностью хода, и начальной разности фаз источников $ \Delta \varphi_0 $:
$ \Delta \varphi = \frac{2\pi}{\lambda} \Delta r + \Delta \varphi_0 $
Поскольку в точке O разность хода $ \Delta r = 0 $, то полная разность фаз равна начальной разности фаз источников: $ \Delta \varphi = \Delta \varphi_0 $.
Условием максимума интерференции является кратность полной разности фаз $ 2\pi $: $ \Delta \varphi = 2\pi k $, где $ k $ — целое число.
В условии задачи сказано, что источники когерентны. Когерентность означает, что начальная разность фаз $ \Delta \varphi_0 $ постоянна во времени, но не обязательно равна нулю. Если источники синфазны (колебания происходят в одинаковой фазе), то $ \Delta \varphi_0 = 0 $, и в точке O будет наблюдаться главный максимум освещенности. Однако если источники находятся в противофазе (сдвиг фаз равен $ \pi $), то $ \Delta \varphi_0 = \pi $, и в точке O будет наблюдаться минимум освещенности. Так как в условии задачи не указана начальная разность фаз источников, однозначно утверждать, что в точке O будет максимум, нельзя.
Ответ: Не обязательно. Максимум в точке O будет наблюдаться только в том случае, если источники являются синфазными (начальная разность фаз равна нулю). Если источники находятся в противофазе, в точке O будет наблюдаться минимум.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 10-11 класс, для упражнения номер 35.5 расположенного на странице 248 к задачнику 2008 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №35.5 (с. 248), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.