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Номер 920, страница 128, часть 1 - гдз по физике 10-11 класс сборник задач Парфентьева
Авторы: Парфентьева Н. А.
Тип: Сборник задач
Серия: классический курс
Издательство: Просвещение
Год издания: 2007 - 2026
Часть: 1
Цвет обложки: фиолетовый
ISBN: 978-5-09-092936-3
Популярные ГДЗ в 10 классе
Часть 1. 11 класс. Оптика. Световые волны. Интерференция света - номер 920, страница 128.
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" => 1320923 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "128" "field_page_end" => null "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-920" "field_display_title" => "920" "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 {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #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" => 1319883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1058 #items: array:1 [ 0 => App\Models\Book {#1057 #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" => 3751 "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 {#1062 #items: array:1 [ 0 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:2 [ 0 => App\Models\Term {#1061 #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 [ …6] "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 [ …6] "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 {#1063 #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 [ …6] "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 [ …6] "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 {#1067 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1074 #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" => 5418 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Парфентьева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Наталия" "field_patronymic" => "Андреевна" "field_surname_rp" => "Парфентьевой" ] #original: array:12 [ "id" => 5418 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Парфентьева" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Наталия" "field_patronymic" => "Андреевна" "field_surname_rp" => "Парфентьевой" ] #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 {#1064 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1069 #items: array:1 [ 0 => App\Models\Term {#1068 #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" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #original: array:10 [ "id" => 6598 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Сборник задач" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "sbornik zadach" ] #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 {#1070 #items: array:1 [ 0 => App\Models\Term {#1071 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1076 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:8 [ "id" => 4718 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "классический курс" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "klassicheskiy kurs" ] #original: array:8 [ "id" => 4718 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "классический курс" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "klassicheskiy kurs" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "13" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Term {#1082 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1110" "field_priority" => null "field_default_folder" => "/fizika_10/parfenteva-sz/" "field_isbn" => "978-5-09-092936-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235" "alt" => "" "width" => "1588" "height" => "2426" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Term {#1088 #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" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ …6] "field_translit" => "fioletovyy" ] #original: array:6 [ "id" => 48 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "фиолетовый" "field_cases" => array:6 [ …6] "field_translit" => "fioletovyy" ] #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" => 3751 "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 {#1062} "field_class" => Illuminate\Database\Eloquent\Collection {#1060} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1067} "field_author" => Illuminate\Database\Eloquent\Collection {#1075} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1064} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1069} "field_country" => Illuminate\Database\Eloquent\Collection {#1070} "field_city" => Illuminate\Database\Eloquent\Collection {#1077} "field_series" => Illuminate\Database\Eloquent\Collection {#1079} "field_umk" => Illuminate\Database\Eloquent\Collection {#1078} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1066} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1083} "field_publication_number" => "13" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1085} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1084} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2007" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "1110" "field_priority" => null "field_default_folder" => "/fizika_10/parfenteva-sz/" "field_isbn" => "978-5-09-092936-3" "field_cover" => array:1 [ 0 => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_10/parfenteva-sz/covers/cover1.webp?ts=1756251235" "alt" => "" "width" => "1588" "height" => "2426" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1081} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1087} "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1091} "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 {#1048 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "5" "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 {#1058} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1048} ] #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 {#1114 #items: array:5 [ 0 => App\Models\Branch {#1126 #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" => 1319883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "5" "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 {#1128 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319883 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1127} "field_page_start" => "5" "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 {#1128} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1129} ] #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 {#1130 #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" => 1319958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "11 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "100" "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 {#1132 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1319958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "11 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1131} "field_page_start" => "100" "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 {#1132} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1133} ] #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 {#1134 #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" => 1319980 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "121" "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 {#1136 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145 #items: array:1 [ 0 => App\Models\Branch {#1144 #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" => 1319958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "11 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "100" "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 {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …2} ] #original: array:24 [ "id" => 1319958 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "11 класс" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_page_start" => "100" "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 {#1147 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 …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" => 1319980 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1135} "field_page_start" => "121" "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 {#1136} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1145} ] #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 {#1138 #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" => 1319981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Световые волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "121" "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 {#1141 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154 #items: array:1 [ 0 => App\Models\Branch {#1153 #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" => 1319980 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_page_start" => "121" "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 {#1156 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 …2} ] #original: array:24 [ "id" => 1319980 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1155 …2} "field_page_start" => "121" "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 {#1156 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1157 …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" => 1319981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Световые волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "121" "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 {#1141} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1154} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Branch {#1142 #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" => 1319984 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Интерференция света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1139 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "128" "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 {#1150 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1163 #items: array:1 [ 0 => App\Models\Branch {#1162 #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" => 1319981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Световые волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_page_start" => "121" "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 {#1165 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1166 …2} ] #original: array:24 [ "id" => 1319981 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Световые волны" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1164 …2} "field_page_start" => "121" "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 {#1165 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1166 …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" => 1319984 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Интерференция света" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1139} "field_page_start" => "128" "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 {#1150} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1163} ] #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 {#1038 #items: array:2 [ 0 => App\Models\Element {#1106 #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" => 1497081 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1097 #items: array:1 [ 0 => App\Models\Edition {#1096 #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" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 …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 {#1090 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093 …2} "field_content_source" => null ] #original: array:21 [ "id" => 5460 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1094 …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 {#1090 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093 …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" => "1320923" "type" => "task" ] "text" => "<p><strong>920.</strong> [763] Определите минимальную толщину воздушного зазора между двумя прозрачными стеклянными пластинками, чтобы стекло при нормальном падении на него света с длиной волны 600 нм в отражённом свете казалось тёмным.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "920-1.jpg" "alt" => null "width" => "1381" "height" => 312 "path" => "/media/fizika_10/parfenteva-sz/0-1/920-1.webp?ts=1756373680" ] ] ] #original: array:7 [ "id" => 1497081 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1097} "task" => array:2 [ "refs" => "1320923" "type" => "task" ] "text" => "<p><strong>920.</strong> [763] Определите минимальную толщину воздушного зазора между двумя прозрачными стеклянными пластинками, чтобы стекло при нормальном падении на него света с длиной волны 600 нм в отражённом свете казалось тёмным.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "920-1.jpg" "alt" => null "width" => "1381" "height" => 312 "path" => "/media/fizika_10/parfenteva-sz/0-1/920-1.webp?ts=1756373680" ] ] ] #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 {#1105 #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" => 1725008 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Edition {#1052 #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" => 6302 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043 …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 {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6302 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1043 …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 {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1051 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1041 …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" => "1320923" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина волны света в вакууме, $\lambda = 600$ нм</p><p>Показатель преломления воздуха, $n \approx 1$</p><p>Падение света нормальное.</p><p>В отражённом свете наблюдается интерференционный минимум (поверхность кажется тёмной).</p><p>$\lambda = 600 \cdot 10^{-9}$ м</p><p><strong>Найти:</strong></p><p>Минимальную толщину воздушного зазора $d_{min}$.</p><p><strong>Решение:</strong></p><p>Наблюдаемое явление объясняется интерференцией световых волн, отражённых от двух поверхностей воздушного зазора. Первая волна отражается от верхней границы зазора (граница стекло-воздух), а вторая — от нижней (граница воздух-стекло).</p><p>Оптическая разность хода ($\Delta$) этих двух волн определяет результат их интерференции. Она складывается из двух компонентов:</p><p><strong>1.</strong> Разность хода, обусловленная прохождением второй волной дополнительного расстояния в воздушном зазоре. При нормальном падении света это расстояние равно удвоенной толщине зазора $2d$. Оптическая разность хода составляет $2dn$, где $\text{n}$ — показатель преломления воздуха.</p><p><strong>2.</strong> Дополнительный сдвиг фаз при отражении света.<br>— При отражении от первой границы (стекло-воздух), свет переходит из оптически более плотной среды в менее плотную ($n_{стекла} > n_{воздуха}$). В этом случае фаза волны не меняется.<br>— При отражении от второй границы (воздух-стекло), свет переходит из оптически менее плотной среды в более плотную ($n_{воздуха} < n_{стекла}$). В этом случае фаза волны меняется на $\pi$, что эквивалентно появлению дополнительной разности хода в половину длины волны ($\lambda/2$).</p><p>Поскольку одна из волн получает дополнительный сдвиг фазы в $\pi$, для того чтобы эти волны погасили друг друга (деструктивная интерференция, тёмная полоса), их оптическая разность хода, создаваемая толщиной плёнки, должна быть равна целому числу длин волн.</p><p>Условие минимума интенсивности в отражённом свете для данного случая:</p><p>$2dn = m\lambda$</p><p>где $\text{m}$ — порядок интерференционного минимума ($m=1, 2, 3, ...$).</p><p>Нам необходимо найти минимальную толщину зазора $d_{min}$, при которой условие выполняется. Минимальная ненулевая толщина соответствует минимальному значению $\text{m}$, то есть $m=1$.</p><p>При $m=1$ получаем:</p><p>$2d_{min}n = 1 \cdot \lambda$</p><p>Отсюда выражаем $d_{min}$:</p><p>$d_{min} = \frac{\lambda}{2n}$</p><p>Показатель преломления воздуха $\text{n}$ принимаем равным 1. Подставим числовые значения:</p><p>$d_{min} = \frac{600 \text{ нм}}{2 \cdot 1} = 300 \text{ нм}$</p><p><strong>Ответ:</strong> минимальная толщина воздушного зазора составляет 300 нм.</p>" ] #original: array:6 [ "id" => 1725008 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1053} "task" => array:2 [ "refs" => "1320923" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Длина волны света в вакууме, $\lambda = 600$ нм</p><p>Показатель преломления воздуха, $n \approx 1$</p><p>Падение света нормальное.</p><p>В отражённом свете наблюдается интерференционный минимум (поверхность кажется тёмной).</p><p>$\lambda = 600 \cdot 10^{-9}$ м</p><p><strong>Найти:</strong></p><p>Минимальную толщину воздушного зазора $d_{min}$.</p><p><strong>Решение:</strong></p><p>Наблюдаемое явление объясняется интерференцией световых волн, отражённых от двух поверхностей воздушного зазора. Первая волна отражается от верхней границы зазора (граница стекло-воздух), а вторая — от нижней (граница воздух-стекло).</p><p>Оптическая разность хода ($\Delta$) этих двух волн определяет результат их интерференции. Она складывается из двух компонентов:</p><p><strong>1.</strong> Разность хода, обусловленная прохождением второй волной дополнительного расстояния в воздушном зазоре. При нормальном падении света это расстояние равно удвоенной толщине зазора $2d$. Оптическая разность хода составляет $2dn$, где $\text{n}$ — показатель преломления воздуха.</p><p><strong>2.</strong> Дополнительный сдвиг фаз при отражении света.<br>— При отражении от первой границы (стекло-воздух), свет переходит из оптически более плотной среды в менее плотную ($n_{стекла} > n_{воздуха}$). В этом случае фаза волны не меняется.<br>— При отражении от второй границы (воздух-стекло), свет переходит из оптически менее плотной среды в более плотную ($n_{воздуха} < n_{стекла}$). В этом случае фаза волны меняется на $\pi$, что эквивалентно появлению дополнительной разности хода в половину длины волны ($\lambda/2$).</p><p>Поскольку одна из волн получает дополнительный сдвиг фазы в $\pi$, для того чтобы эти волны погасили друг друга (деструктивная интерференция, тёмная полоса), их оптическая разность хода, создаваемая толщиной плёнки, должна быть равна целому числу длин волн.</p><p>Условие минимума интенсивности в отражённом свете для данного случая:</p><p>$2dn = m\lambda$</p><p>где $\text{m}$ — порядок интерференционного минимума ($m=1, 2, 3, ...$).</p><p>Нам необходимо найти минимальную толщину зазора $d_{min}$, при которой условие выполняется. Минимальная ненулевая толщина соответствует минимальному значению $\text{m}$, то есть $m=1$.</p><p>При $m=1$ получаем:</p><p>$2d_{min}n = 1 \cdot \lambda$</p><p>Отсюда выражаем $d_{min}$:</p><p>$d_{min} = \frac{\lambda}{2n}$</p><p>Показатель преломления воздуха $\text{n}$ принимаем равным 1. Подставим числовые значения:</p><p>$d_{min} = \frac{600 \text{ нм}}{2 \cdot 1} = 300 \text{ нм}$</p><p><strong>Ответ:</strong> минимальная толщина воздушного зазора составляет 300 нм.</p>" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1320924" "type" => "task" ] "previous" => array:2 [ "refs" => "1320922" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1057} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\BookPage {#1111 #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" => 1341378 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "128" "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/page-128" "field_display_title" => "128" "field_folder" => "1" "field_image_name" => "128" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1104 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1100 #items: array:1 [ 0 => App\Models\Book {#1057} ] #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 {#1102 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1121 #items: array:1 [ 0 => App\Models\Element {#1123 #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" => 1516593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1122 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1516593 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1122 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1341379" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1341377" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:8 [ 0 => App\Models\Task {#1257 #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" => 1320919 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "128" "field_page_end" => null "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-916" "field_display_title" => "916" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1259 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1260 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1261 …2} "content" => Illuminate\Database\Eloquent\Collection {#1263 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1269 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1320919 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "128" "field_page_end" => null "field_url" => "/10-klass/fizika/parfenteva-sbornik-zadach/1-916" "field_display_title" => "916" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1258 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null 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№920 (с. 128)
Условие. №920 (с. 128)
скриншот условия
920. [763] Определите минимальную толщину воздушного зазора между двумя прозрачными стеклянными пластинками, чтобы стекло при нормальном падении на него света с длиной волны 600 нм в отражённом свете казалось тёмным.
Решение. №920 (с. 128)
Дано:
Длина волны света в вакууме, $\lambda = 600$ нм
Показатель преломления воздуха, $n \approx 1$
Падение света нормальное.
В отражённом свете наблюдается интерференционный минимум (поверхность кажется тёмной).
$\lambda = 600 \cdot 10^{-9}$ м
Найти:
Минимальную толщину воздушного зазора $d_{min}$.
Решение:
Наблюдаемое явление объясняется интерференцией световых волн, отражённых от двух поверхностей воздушного зазора. Первая волна отражается от верхней границы зазора (граница стекло-воздух), а вторая — от нижней (граница воздух-стекло).
Оптическая разность хода ($\Delta$) этих двух волн определяет результат их интерференции. Она складывается из двух компонентов:
1. Разность хода, обусловленная прохождением второй волной дополнительного расстояния в воздушном зазоре. При нормальном падении света это расстояние равно удвоенной толщине зазора $2d$. Оптическая разность хода составляет $2dn$, где $\text{n}$ — показатель преломления воздуха.
2. Дополнительный сдвиг фаз при отражении света.
— При отражении от первой границы (стекло-воздух), свет переходит из оптически более плотной среды в менее плотную ($n_{стекла} > n_{воздуха}$). В этом случае фаза волны не меняется.
— При отражении от второй границы (воздух-стекло), свет переходит из оптически менее плотной среды в более плотную ($n_{воздуха} < n_{стекла}$). В этом случае фаза волны меняется на $\pi$, что эквивалентно появлению дополнительной разности хода в половину длины волны ($\lambda/2$).
Поскольку одна из волн получает дополнительный сдвиг фазы в $\pi$, для того чтобы эти волны погасили друг друга (деструктивная интерференция, тёмная полоса), их оптическая разность хода, создаваемая толщиной плёнки, должна быть равна целому числу длин волн.
Условие минимума интенсивности в отражённом свете для данного случая:
$2dn = m\lambda$
где $\text{m}$ — порядок интерференционного минимума ($m=1, 2, 3, ...$).
Нам необходимо найти минимальную толщину зазора $d_{min}$, при которой условие выполняется. Минимальная ненулевая толщина соответствует минимальному значению $\text{m}$, то есть $m=1$.
При $m=1$ получаем:
$2d_{min}n = 1 \cdot \lambda$
Отсюда выражаем $d_{min}$:
$d_{min} = \frac{\lambda}{2n}$
Показатель преломления воздуха $\text{n}$ принимаем равным 1. Подставим числовые значения:
$d_{min} = \frac{600 \text{ нм}}{2 \cdot 1} = 300 \text{ нм}$
Ответ: минимальная толщина воздушного зазора составляет 300 нм.
Другие задания:
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