gdz.top
Номер 141, страница 253 - 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. Олимпиадные задачи - номер 141, страница 253.
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" => 1319801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#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 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:2 [ …2] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:3 [ …3] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1059 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1060 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065 #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 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1041} "field_class" => Illuminate\Database\Eloquent\Collection {#1043} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046} "field_author" => Illuminate\Database\Eloquent\Collection {#1048} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053} "field_country" => Illuminate\Database\Eloquent\Collection {#1055} "field_city" => Illuminate\Database\Eloquent\Collection {#1057} "field_series" => Illuminate\Database\Eloquent\Collection {#1059} "field_umk" => Illuminate\Database\Eloquent\Collection {#1060} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1061} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1065} "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 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1066} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1068} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1069} "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 } "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 {#1192 #items: array:4 [ 0 => App\Models\Branch {#1202 #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 {#1203 #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 {#1237 #items: array:1 [ 0 => App\Models\Book {#1204 #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 {#1206 #items: array:1 [ 0 => App\Models\Term {#1205 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:2 [ 0 => App\Models\Term {#1208 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #original: array:6 [ "id" => 5459 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "10" "field_cases" => array:6 [ "field_accusative_case" => "десятый" "field_creative_case" => "десятым" "field_dative_case" => "десятому" "field_genitive_case" => "десятого" "field_nominative_case" => "десятый" "field_prepositional_case" => "десятом" ] "field_translit" => "desjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1209 #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" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #original: array:6 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "11" "field_cases" => array:6 [ "field_accusative_case" => "одиннадцатый" "field_creative_case" => "одиннадцатым" "field_dative_case" => "одиннадцатому" "field_genitive_case" => "одинадцатого" "field_nominative_case" => "одинадцатый" "field_prepositional_case" => "одиннадцатом" ] "field_translit" => "odinadcatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1210 #items: array:1 [ 0 => App\Models\Term {#1211 #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" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #original: array:6 [ "id" => 5158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Илекса" "field_cases" => null "field_translit" => "ileksa" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1212 #items: array:3 [ 0 => App\Models\Term {#1213 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #original: array:12 [ "id" => 4102 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Гельфгат" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Илья" "field_patronymic" => "Маркович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1214 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #original: array:12 [ "id" => 4104 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Генденштейн" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Лев" "field_patronymic" => "Элевич" "field_surname_rp" => "Генденштейна" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1215 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Кирик" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Леонид" "field_patronymic" => "Анатольевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1216 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1217 #items: array:1 [ 0 => App\Models\Term {#1218 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #original: array:10 [ "id" => 6518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Задачник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "задачник" "field_creative_case" => "задачником" "field_dative_case" => "задачнику" "field_genitive_case" => "задачника" "field_nominative_case" => "задачник" "field_prepositional_case" => "задачнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "zadachnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Term {#1220 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Term {#1222 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1223 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1224 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:1 [ 0 => App\Models\Term {#1226 #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" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #original: array:6 [ "id" => 40 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "профильный" "field_cases" => array:6 [ "field_accusative_case" => "профильный" "field_creative_case" => "профильным" "field_dative_case" => "профильному" "field_genitive_case" => "профильного" "field_nominative_case" => "профильный" "field_prepositional_case" => "профильном" ] "field_translit" => "profilnyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1227 #items: [] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1228 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1229 #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 {#1230 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1231 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1232 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:1 [ 0 => App\Models\Term {#1234 #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" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #original: array:6 [ "id" => 46 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "красный" "field_cases" => array:6 [ "field_accusative_case" => "красный" "field_creative_case" => "красным" "field_dative_case" => "красному" "field_genitive_case" => "красного" "field_nominative_case" => "красный" "field_prepositional_case" => "красном" ] "field_translit" => "krasnyy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 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 {#1206} "field_class" => Illuminate\Database\Eloquent\Collection {#1207} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1210} "field_author" => Illuminate\Database\Eloquent\Collection {#1212} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1216} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1217} "field_country" => Illuminate\Database\Eloquent\Collection {#1219} "field_city" => Illuminate\Database\Eloquent\Collection {#1221} "field_series" => Illuminate\Database\Eloquent\Collection {#1223} "field_umk" => Illuminate\Database\Eloquent\Collection {#1224} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1225} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1227} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1228} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1229} "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 {#1230} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1231} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1232} "field_url" => "/10-klass/fizika/gelfgat-zadachnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1233} "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 } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1235 #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 {#1203} "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 {#1237} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1235} ] #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 {#1236 #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 {#1238 #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 {#1239 #items: array:1 [ 0 => App\Models\Book {#1204} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1240 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #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 {#1238} "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 {#1239} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1240} ] #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 {#1241 #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 {#1242 #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 {#1243 #items: array:1 [ 0 => App\Models\Book {#1204} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1285 #items: array:1 [ 0 => App\Models\Branch {#1244 #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 {#1246 #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 {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ …1] #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 {#1246} "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 {#1245} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1278} ] #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 {#1242} "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 {#1243} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1285} ] #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 {#1283 #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" => 1319378 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1284 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "251" "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 {#1286 #items: array:1 [ 0 => App\Models\Book {#1204} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1332 #items: array:1 [ 0 => App\Models\Branch {#1287 #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 {#1289 #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 {#1288 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1321 #items: array:1 [ …1] #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 {#1289} "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 {#1288} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1321} ] #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" => 1319378 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Олимпиадные задачи" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1284} "field_page_start" => "251" "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 {#1286} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1332} ] #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 {#1147 #items: array:2 [ 0 => App\Models\Element {#1180 #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" => 1494119 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ 0 => App\Models\Edition {#1178 #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 {#1176 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1175 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1174 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173 #items: [] #escapeWhenCastingToString: false } "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 {#1176} "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 {#1175} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1174} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1173} "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" => "1319801" "type" => "task" ] "text" => "<p><strong>O41.</strong> Собирающая линза с фокусным расстоянием $F = 10$ см разрезана по диаметру, и части линзы раздвинуты на расстояние $h = 0,5$ мм. Перед линзой на расстоянии $d = 15$ см находится точечный источник монохроматического света с длиной волны $\lambda = 500$ нм. Оцените число $\text{N}$ светлых интерференционных полос на экране, расположенном за линзой на расстоянии $L = 60$ см. Промежуток между частями линзы закрыт непрозрачной перегородкой.</p><p>☑ $N \approx 25$.</p><p><strong><em>Решение.</em></strong> Раздвинутые части линзы дают два изображения $A_1$ и $A_2$ источника $\text{A}$ (см. рисунок) на расстоянии $H = \frac{hd}{d - F}$ друг от друга и на расстоянии $L_1 = L - \frac{dF}{d - F}$ от экрана.</p><p>Ширина полосы перекрытия на экране двух световых пучков $a = h(L + d)/d$. Поскольку ширина интерференционных полос на экране $x = \lambda L_1/H$ (см. задачу 35.5), получаем $N \approx a/x \approx 25$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "141-1.jpg" "alt" => null "width" => "1408" "height" => 1465 "path" => "/media/fizika_10/gelfgat-z/0-olimp/141-1.webp?ts=1756251279" ] ] ] #original: array:7 [ "id" => 1494119 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1170} "task" => array:2 [ "refs" => "1319801" "type" => "task" ] "text" => "<p><strong>O41.</strong> Собирающая линза с фокусным расстоянием $F = 10$ см разрезана по диаметру, и части линзы раздвинуты на расстояние $h = 0,5$ мм. Перед линзой на расстоянии $d = 15$ см находится точечный источник монохроматического света с длиной волны $\lambda = 500$ нм. Оцените число $\text{N}$ светлых интерференционных полос на экране, расположенном за линзой на расстоянии $L = 60$ см. Промежуток между частями линзы закрыт непрозрачной перегородкой.</p><p>☑ $N \approx 25$.</p><p><strong><em>Решение.</em></strong> Раздвинутые части линзы дают два изображения $A_1$ и $A_2$ источника $\text{A}$ (см. рисунок) на расстоянии $H = \frac{hd}{d - F}$ друг от друга и на расстоянии $L_1 = L - \frac{dF}{d - F}$ от экрана.</p><p>Ширина полосы перекрытия на экране двух световых пучков $a = h(L + d)/d$. Поскольку ширина интерференционных полос на экране $x = \lambda L_1/H$ (см. задачу 35.5), получаем $N \approx a/x \approx 25$.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "141-1.jpg" "alt" => null "width" => "1408" "height" => 1465 "path" => "/media/fizika_10/gelfgat-z/0-olimp/141-1.webp?ts=1756251279" ] ] ] #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 {#1171 #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" => 1691676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ 0 => App\Models\Edition {#1172 #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 {#1167 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1168 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1165 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166 #items: [] #escapeWhenCastingToString: false } "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 {#1167} "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 {#1168} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1165} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166} "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" => "1319801" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>Фокусное расстояние линзы, $F = 10 \text{ см}$<br>Расстояние, на которое раздвинуты части линзы, $h = 0,5 \text{ мм}$<br>Расстояние от источника до линзы, $d = 15 \text{ см}$<br>Длина волны света, $\lambda = 500 \text{ нм}$<br>Расстояние от линзы до экрана, $L = 60 \text{ см}$</p><p>$F = 0,1 \text{ м}$<br>$h = 0,5 \cdot 10^{-3} \text{ м}$<br>$d = 0,15 \text{ м}$<br>$\lambda = 500 \cdot 10^{-9} \text{ м} = 5 \cdot 10^{-7} \text{ м}$<br>$L = 0,6 \text{ м}$</p><p><strong>Найти:</strong><br>Число светлых интерференционных полос, $N$.</p><p><strong>Решение:</strong><br>Данная оптическая система аналогична опыту Юнга с двумя щелями. Две половины собирающей линзы создают два мнимых когерентных источника света $A_1$ и $A_2$ из одного реального источника $A$. Свет от этих двух источников интерферирует на экране.<br><br>1. Найдем положение мнимых источников.Расстояние от линзы до изображений $f'$ определяется формулой тонкой линзы:<br>$\frac{1}{d} + \frac{1}{f'} = \frac{1}{F}$<br>Отсюда расстояние до изображений:<br>$f' = \frac{dF}{d-F} = \frac{15 \text{ см} \cdot 10 \text{ см}}{15 \text{ см} - 10 \text{ см}} = \frac{150}{5} \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.<br>Изображения $A_1$ и $A_2$ находятся на расстоянии $f' = 30$ см за линзой.<br><br>2. Найдем расстояние $H$ между мнимыми источниками $A_1$ и $A_2$.Каждая половина линзы смещена на $h/2$ от главной оптической оси. Это приводит к смещению изображений. Расстояние между изображениями определяется по формуле:<br>$H = \frac{hd}{d-F} = \frac{(0,5 \cdot 10^{-3} \text{ м}) \cdot 0,15 \text{ м}}{0,15 \text{ м} - 0,1 \text{ м}} = \frac{0,075 \cdot 10^{-3}}{0,05} \text{ м} = 1,5 \cdot 10^{-3} \text{ м}$.<br><br>3. Найдем расстояние $L_1$ от мнимых источников до экрана.<br>$L_1 = L - f' = 60 \text{ см} - 30 \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.<br><br>4. Определим ширину интерференционной полосы $x$ на экране.Ширина светлой (или темной) полосы в опыте Юнга вычисляется по формуле:<br>$x = \frac{\lambda L_1}{H} = \frac{(5 \cdot 10^{-7} \text{ м}) \cdot 0,3 \text{ м}}{1,5 \cdot 10^{-3} \text{ м}} = \frac{1,5 \cdot 10^{-7}}{1,5 \cdot 10^{-3}} \text{ м} = 10^{-4} \text{ м} = 0,1 \text{ мм}$.<br><br>5. Найдем ширину области $a$, где наблюдается интерференция.Эта область представляет собой зону перекрытия световых пучков от двух половин линзы. Ее ширину можно оценить из геометрических соображений (подобие треугольников, образованных лучами от источника, проходящими через центры половин линз):<br>$a = h \frac{L+d}{d} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,6 \text{ м} + 0,15 \text{ м}}{0,15 \text{ м}} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,75}{0,15} = (0,5 \cdot 10^{-3} \text{ м}) \cdot 5 = 2,5 \cdot 10^{-3} \text{ м} = 2,5 \text{ мм}$.<br><br>6. Оценим число светлых интерференционных полос $N$.Число полос равно отношению ширины области интерференции к ширине одной полосы:<br>$N = \frac{a}{x} = \frac{2,5 \cdot 10^{-3} \text{ м}}{10^{-4} \text{ м}} = 25$.</p><p><strong>Ответ:</strong> $N = 25$.</p>" ] #original: array:6 [ "id" => 1691676 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1162} "task" => array:2 [ "refs" => "1319801" "type" => "task" ] "text" => "<p><strong>Дано:</strong><br>Фокусное расстояние линзы, $F = 10 \text{ см}$<br>Расстояние, на которое раздвинуты части линзы, $h = 0,5 \text{ мм}$<br>Расстояние от источника до линзы, $d = 15 \text{ см}$<br>Длина волны света, $\lambda = 500 \text{ нм}$<br>Расстояние от линзы до экрана, $L = 60 \text{ см}$</p><p>$F = 0,1 \text{ м}$<br>$h = 0,5 \cdot 10^{-3} \text{ м}$<br>$d = 0,15 \text{ м}$<br>$\lambda = 500 \cdot 10^{-9} \text{ м} = 5 \cdot 10^{-7} \text{ м}$<br>$L = 0,6 \text{ м}$</p><p><strong>Найти:</strong><br>Число светлых интерференционных полос, $N$.</p><p><strong>Решение:</strong><br>Данная оптическая система аналогична опыту Юнга с двумя щелями. Две половины собирающей линзы создают два мнимых когерентных источника света $A_1$ и $A_2$ из одного реального источника $A$. Свет от этих двух источников интерферирует на экране.<br><br>1. Найдем положение мнимых источников.Расстояние от линзы до изображений $f'$ определяется формулой тонкой линзы:<br>$\frac{1}{d} + \frac{1}{f'} = \frac{1}{F}$<br>Отсюда расстояние до изображений:<br>$f' = \frac{dF}{d-F} = \frac{15 \text{ см} \cdot 10 \text{ см}}{15 \text{ см} - 10 \text{ см}} = \frac{150}{5} \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.<br>Изображения $A_1$ и $A_2$ находятся на расстоянии $f' = 30$ см за линзой.<br><br>2. Найдем расстояние $H$ между мнимыми источниками $A_1$ и $A_2$.Каждая половина линзы смещена на $h/2$ от главной оптической оси. Это приводит к смещению изображений. Расстояние между изображениями определяется по формуле:<br>$H = \frac{hd}{d-F} = \frac{(0,5 \cdot 10^{-3} \text{ м}) \cdot 0,15 \text{ м}}{0,15 \text{ м} - 0,1 \text{ м}} = \frac{0,075 \cdot 10^{-3}}{0,05} \text{ м} = 1,5 \cdot 10^{-3} \text{ м}$.<br><br>3. Найдем расстояние $L_1$ от мнимых источников до экрана.<br>$L_1 = L - f' = 60 \text{ см} - 30 \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.<br><br>4. Определим ширину интерференционной полосы $x$ на экране.Ширина светлой (или темной) полосы в опыте Юнга вычисляется по формуле:<br>$x = \frac{\lambda L_1}{H} = \frac{(5 \cdot 10^{-7} \text{ м}) \cdot 0,3 \text{ м}}{1,5 \cdot 10^{-3} \text{ м}} = \frac{1,5 \cdot 10^{-7}}{1,5 \cdot 10^{-3}} \text{ м} = 10^{-4} \text{ м} = 0,1 \text{ мм}$.<br><br>5. Найдем ширину области $a$, где наблюдается интерференция.Эта область представляет собой зону перекрытия световых пучков от двух половин линзы. Ее ширину можно оценить из геометрических соображений (подобие треугольников, образованных лучами от источника, проходящими через центры половин линз):<br>$a = h \frac{L+d}{d} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,6 \text{ м} + 0,15 \text{ м}}{0,15 \text{ м}} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,75}{0,15} = (0,5 \cdot 10^{-3} \text{ м}) \cdot 5 = 2,5 \cdot 10^{-3} \text{ м} = 2,5 \text{ мм}$.<br><br>6. Оценим число светлых интерференционных полос $N$.Число полос равно отношению ширины области интерференции к ширине одной полосы:<br>$N = \frac{a}{x} = \frac{2,5 \cdot 10^{-3} \text{ м}}{10^{-4} \text{ м}} = 25$.</p><p><strong>Ответ:</strong> $N = 25$.</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" => "1319802" "type" => "task" ] "previous" => array:2 [ "refs" => "1319800" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:1 [ 0 => App\Models\Book {#1204} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\BookPage {#1189 #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" => 1341214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-253" "field_display_title" => "253" "field_folder" => "1" "field_image_name" => "253" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1163 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => App\Models\Book {#1204} ] #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 {#1158 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1152 #items: array:1 [ 0 => App\Models\Element {#1151 #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" => 1519759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1187 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1341214" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1519759 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1187} "book_page" => array:2 [ "refs" => "1341214" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1341215" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341213" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1426 #items: array:3 [ 0 => App\Models\Task {#1436 #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" => 1319800 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => "253" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-140" "field_display_title" => "140" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1437 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1438 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1440 #items: array:4 [ …4] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1442 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319801" "type" => "task" ] "previous" => array:2 [ "refs" => "1319799" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1448 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341213" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319800 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "252" "field_page_end" => "253" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-140" "field_display_title" => "140" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1437} "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 {#1438} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1439} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1440} "content" => Illuminate\Database\Eloquent\Collection {#1442} "next" => array:2 [ "refs" => "1319801" "type" => "task" ] "previous" => array:2 [ "refs" => "1319799" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1448} "page" => array:2 [ "refs" => "1341213" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1443 #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" => 1319801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1441 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1450 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1446 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1444 #items: array:4 [ …4] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1447 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1319802" "type" => "task" ] "previous" => array:2 [ "refs" => "1319800" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1445 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1341214" "type" => "book_page" ] ] #original: array:24 [ "id" => 1319801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1441} "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 {#1450} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1446} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1444} "content" => Illuminate\Database\Eloquent\Collection {#1447} "next" => array:2 [ "refs" => "1319802" "type" => "task" ] "previous" => array:2 [ "refs" => "1319800" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1445} "page" => array:2 [ "refs" => "1341214" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1455 #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" => 1319802 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => "254" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-142" "field_display_title" => "142" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1456 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1457 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1458 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1459 #items: array:4 [ …4] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1461 #items: array:2 [ …2] …1 } "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1467 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1319802 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => "254" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-142" "field_display_title" => "142" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1456} "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 {#1457} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1458} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1459} "content" => Illuminate\Database\Eloquent\Collection {#1461 …1} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1467 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1341214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_url" => "/10-klass/fizika/gelfgat-zadachnik/page-253" "field_display_title" => "253" "field_folder" => "1" "field_image_name" => "253" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1163} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1164} "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 {#1158} "content" => Illuminate\Database\Eloquent\Collection {#1152} "next" => array:2 [ "refs" => "1341215" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341213" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1426} ] #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" => 1319801 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "253" "field_page_end" => null "field_url" => "/10-klass/fizika/gelfgat-zadachnik/olimp-141" "field_display_title" => "141" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1074} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1192} "content" => Illuminate\Database\Eloquent\Collection {#1147} "next" => array:2 [ "refs" => "1319802" "type" => "task" ] "previous" => array:2 [ "refs" => "1319800" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1188} "page" => array:2 [ "refs" => "1341214" "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 => "*" ] }
№141 (с. 253)
Условие. №141 (с. 253)
скриншот условия
O41. Собирающая линза с фокусным расстоянием $F = 10$ см разрезана по диаметру, и части линзы раздвинуты на расстояние $h = 0,5$ мм. Перед линзой на расстоянии $d = 15$ см находится точечный источник монохроматического света с длиной волны $\lambda = 500$ нм. Оцените число $\text{N}$ светлых интерференционных полос на экране, расположенном за линзой на расстоянии $L = 60$ см. Промежуток между частями линзы закрыт непрозрачной перегородкой.
☑ $N \approx 25$.
Решение. Раздвинутые части линзы дают два изображения $A_1$ и $A_2$ источника $\text{A}$ (см. рисунок) на расстоянии $H = \frac{hd}{d - F}$ друг от друга и на расстоянии $L_1 = L - \frac{dF}{d - F}$ от экрана.
Ширина полосы перекрытия на экране двух световых пучков $a = h(L + d)/d$. Поскольку ширина интерференционных полос на экране $x = \lambda L_1/H$ (см. задачу 35.5), получаем $N \approx a/x \approx 25$.
Решение. №141 (с. 253)
Дано:
Фокусное расстояние линзы, $F = 10 \text{ см}$
Расстояние, на которое раздвинуты части линзы, $h = 0,5 \text{ мм}$
Расстояние от источника до линзы, $d = 15 \text{ см}$
Длина волны света, $\lambda = 500 \text{ нм}$
Расстояние от линзы до экрана, $L = 60 \text{ см}$
$F = 0,1 \text{ м}$
$h = 0,5 \cdot 10^{-3} \text{ м}$
$d = 0,15 \text{ м}$
$\lambda = 500 \cdot 10^{-9} \text{ м} = 5 \cdot 10^{-7} \text{ м}$
$L = 0,6 \text{ м}$
Найти:
Число светлых интерференционных полос, $N$.
Решение:
Данная оптическая система аналогична опыту Юнга с двумя щелями. Две половины собирающей линзы создают два мнимых когерентных источника света $A_1$ и $A_2$ из одного реального источника $A$. Свет от этих двух источников интерферирует на экране.
1. Найдем положение мнимых источников.Расстояние от линзы до изображений $f'$ определяется формулой тонкой линзы:
$\frac{1}{d} + \frac{1}{f'} = \frac{1}{F}$
Отсюда расстояние до изображений:
$f' = \frac{dF}{d-F} = \frac{15 \text{ см} \cdot 10 \text{ см}}{15 \text{ см} - 10 \text{ см}} = \frac{150}{5} \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.
Изображения $A_1$ и $A_2$ находятся на расстоянии $f' = 30$ см за линзой.
2. Найдем расстояние $H$ между мнимыми источниками $A_1$ и $A_2$.Каждая половина линзы смещена на $h/2$ от главной оптической оси. Это приводит к смещению изображений. Расстояние между изображениями определяется по формуле:
$H = \frac{hd}{d-F} = \frac{(0,5 \cdot 10^{-3} \text{ м}) \cdot 0,15 \text{ м}}{0,15 \text{ м} - 0,1 \text{ м}} = \frac{0,075 \cdot 10^{-3}}{0,05} \text{ м} = 1,5 \cdot 10^{-3} \text{ м}$.
3. Найдем расстояние $L_1$ от мнимых источников до экрана.
$L_1 = L - f' = 60 \text{ см} - 30 \text{ см} = 30 \text{ см} = 0,3 \text{ м}$.
4. Определим ширину интерференционной полосы $x$ на экране.Ширина светлой (или темной) полосы в опыте Юнга вычисляется по формуле:
$x = \frac{\lambda L_1}{H} = \frac{(5 \cdot 10^{-7} \text{ м}) \cdot 0,3 \text{ м}}{1,5 \cdot 10^{-3} \text{ м}} = \frac{1,5 \cdot 10^{-7}}{1,5 \cdot 10^{-3}} \text{ м} = 10^{-4} \text{ м} = 0,1 \text{ мм}$.
5. Найдем ширину области $a$, где наблюдается интерференция.Эта область представляет собой зону перекрытия световых пучков от двух половин линзы. Ее ширину можно оценить из геометрических соображений (подобие треугольников, образованных лучами от источника, проходящими через центры половин линз):
$a = h \frac{L+d}{d} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,6 \text{ м} + 0,15 \text{ м}}{0,15 \text{ м}} = (0,5 \cdot 10^{-3} \text{ м}) \cdot \frac{0,75}{0,15} = (0,5 \cdot 10^{-3} \text{ м}) \cdot 5 = 2,5 \cdot 10^{-3} \text{ м} = 2,5 \text{ мм}$.
6. Оценим число светлых интерференционных полос $N$.Число полос равно отношению ширины области интерференции к ширине одной полосы:
$N = \frac{a}{x} = \frac{2,5 \cdot 10^{-3} \text{ м}}{10^{-4} \text{ м}} = 25$.
Ответ: $N = 25$.
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 141 расположенного на странице 253 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 №141 (с. 253), авторов: Гельфгат (Илья Маркович), Генденштейн (Лев Элевич), Кирик (Леонид Анатольевич), профильный уровень обучения учебного пособия издательства Илекса.