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Номер 10, страница 43, часть 3 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 3
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 3. Глава 8. Оптика. Параграф 47. Тонкие линзы - номер 10, страница 43.
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" => 1435296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-10" "field_display_title" => "10" "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" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#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 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #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 {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #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 {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#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:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => 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:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1064 #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" => 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 {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #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 {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #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:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #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:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "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" => "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 {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #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:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #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:3 [ 0 => App\Models\Branch {#1124 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1125} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1126} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1127} ] #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 {#1128 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132 #items: array:1 [ 0 => App\Models\Term {#1129 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1132} "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1131} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1130} ] #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 {#1133 #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" => 1434861 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тонкие линзы" "field_branch_order" => "47" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137 #items: array:1 [ 0 => App\Models\Term {#1134 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "40" "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 {#1049} ] #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" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1147 #items: array:1 [ …1] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ …1] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1146} "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1147} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1148} ] #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" => 1434861 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тонкие линзы" "field_branch_order" => "47" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1137} "field_page_start" => "40" "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 => "*" ] } ] #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" => 1698684 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Edition {#1104 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102 #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 {#1103 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1102} "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 {#1103} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1101} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1100} "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" => "1435296" "type" => "task" ] "text" => "<p><strong>10.</strong> На рис. 47 показаны главные оптические оси тонкой собирающей (а) и тонкой рассеивающей (б) линз. Точками обозначены главные фокусы $\text{F}$ этих линз. Цифрой $1'$ обозначены лучи света, выходящие из линз. Постройте ход этих лучей до их преломления в линзах.</p><p><strong>а</strong></p><p><strong>б</strong></p><p>Рис. 47</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1948" "height" => 761 "path" => "/media/fizika_09/grachev-rt/0-47/10-1.webp?ts=1759402865" ] ] ] #original: array:7 [ "id" => 1698684 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1098} "task" => array:2 [ "refs" => "1435296" "type" => "task" ] "text" => "<p><strong>10.</strong> На рис. 47 показаны главные оптические оси тонкой собирающей (а) и тонкой рассеивающей (б) линз. Точками обозначены главные фокусы $\text{F}$ этих линз. Цифрой $1'$ обозначены лучи света, выходящие из линз. Постройте ход этих лучей до их преломления в линзах.</p><p><strong>а</strong></p><p><strong>б</strong></p><p>Рис. 47</p>" "img" => array:1 [ 0 => array:5 [ "name" => "10-1.jpg" "alt" => null "width" => "1948" "height" => 761 "path" => "/media/fizika_09/grachev-rt/0-47/10-1.webp?ts=1759402865" ] ] ] #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 {#1099 #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" => 1734670 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1097 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #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 {#1093 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1093} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092} "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" => "1435296" "type" => "task" ] "text" => "<p>Для построения хода лучей до их преломления в линзах используется свойство побочных фокусов и принцип обратимости световых лучей. Любой пучок параллельных лучей, падающих на линзу, после преломления собирается в одной точке фокальной плоскости (для собирающей линзы) или расходится так, как будто вышел из одной точки фокальной плоскости (для рассеивающей линзы). Эта точка называется побочным фокусом. Луч, проходящий через оптический центр, не меняет своего направления и определяет, какому побочному фокусу соответствует данное направление параллельных лучей.</p><p>Для нахождения падающего луча по известному преломленному лучу необходимо выполнить обратное построение.</p><strong>а</strong><p>В случае с собирающей линзой, все лучи, параллельные некоторому направлению, после преломления собираются в одной точке (побочном фокусе), лежащей в задней фокальной плоскости (плоскости, проходящей через задний фокус F перпендикулярно главной оптической оси).</p><p>1. Найдём точку F' — пересечение преломлённого луча 1' с задней фокальной плоскостью. Это и есть побочный фокус.<br>2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.<br>3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение для собирающей линзы"></p><p><strong>Ответ:</strong> Построение падающего луча показано на рисунке.</p><strong>б</strong><p>В случае с рассеивающей линзой, продолжения всех преломлённых лучей, соответствующих параллельному пучку падающих лучей, пересекаются в одной точке (мнимом побочном фокусе), лежащей в передней фокальной плоскости (плоскости, проходящей через передний фокус F).</p><p>1. Найдём точку F' — пересечение продолжения преломлённого луча 1' с передней фокальной плоскостью. Это мнимый побочный фокус.<br>2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.<br>3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение для рассеивающей линзы"></p><p><strong>Ответ:</strong> Построение падающего луча показано на рисунке.</p>" ] #original: array:6 [ "id" => 1734670 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1435296" "type" => "task" ] "text" => "<p>Для построения хода лучей до их преломления в линзах используется свойство побочных фокусов и принцип обратимости световых лучей. Любой пучок параллельных лучей, падающих на линзу, после преломления собирается в одной точке фокальной плоскости (для собирающей линзы) или расходится так, как будто вышел из одной точки фокальной плоскости (для рассеивающей линзы). Эта точка называется побочным фокусом. Луч, проходящий через оптический центр, не меняет своего направления и определяет, какому побочному фокусу соответствует данное направление параллельных лучей.</p><p>Для нахождения падающего луча по известному преломленному лучу необходимо выполнить обратное построение.</p><strong>а</strong><p>В случае с собирающей линзой, все лучи, параллельные некоторому направлению, после преломления собираются в одной точке (побочном фокусе), лежащей в задней фокальной плоскости (плоскости, проходящей через задний фокус F перпендикулярно главной оптической оси).</p><p>1. Найдём точку F' — пересечение преломлённого луча 1' с задней фокальной плоскостью. Это и есть побочный фокус.<br>2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.<br>3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение для собирающей линзы"></p><p><strong>Ответ:</strong> Построение падающего луча показано на рисунке.</p><strong>б</strong><p>В случае с рассеивающей линзой, продолжения всех преломлённых лучей, соответствующих параллельному пучку падающих лучей, пересекаются в одной точке (мнимом побочном фокусе), лежащей в передней фокальной плоскости (плоскости, проходящей через передний фокус F).</p><p>1. Найдём точку F' — пересечение продолжения преломлённого луча 1' с передней фокальной плоскостью. Это мнимый побочный фокус.<br>2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.<br>3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение для рассеивающей линзы"></p><p><strong>Ответ:</strong> Построение падающего луча показано на рисунке.</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" => "1435297" "type" => "task" ] "previous" => array:2 [ "refs" => "1435295" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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" => 1435678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-43" "field_display_title" => "43" "field_folder" => "3" "field_image_name" => "43" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1087 #items: array:1 [ 0 => App\Models\Branch {#1124} ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1091 #items: array:1 [ 0 => App\Models\Book {#1049} ] #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 {#1089 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Element {#1039 #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" => 1699065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113 #items: array:1 [ …1] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1435678" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ …5] ] ] #original: array:6 [ "id" => 1699065 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1113} "book_page" => array:2 [ "refs" => "1435678" "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" => "1435679" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435677" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:4 [ 0 => App\Models\Task {#1221 #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" => 1435295 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1222 #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 {#1223 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1225 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435296" "type" => "task" ] "previous" => array:2 [ "refs" => "1435294" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1435678" "type" => "book_page" ] ] #original: array:24 [ "id" => 1435295 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1222} "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 {#1223} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1224} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1225} "content" => Illuminate\Database\Eloquent\Collection {#1227} "next" => array:2 [ "refs" => "1435296" "type" => "task" ] "previous" => array:2 [ "refs" => "1435294" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1233} "page" => array:2 [ "refs" => "1435678" "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 {#1228 #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" => 1435296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226 #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 {#1235 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435297" "type" => "task" ] "previous" => array:2 [ "refs" => "1435295" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1435678" "type" => "book_page" ] ] #original: array:24 [ "id" => 1435296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1226} "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 {#1235} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1229} "content" => Illuminate\Database\Eloquent\Collection {#1232} "next" => array:2 [ "refs" => "1435297" "type" => "task" ] "previous" => array:2 [ "refs" => "1435295" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1230} "page" => array:2 [ "refs" => "1435678" "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 {#1240 #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" => 1435297 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241 #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 {#1242 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:3 [ …3] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435298" "type" => "task" ] "previous" => array:2 [ "refs" => "1435296" …1 ] "book" => Illuminate\Database\Eloquent\Collection {#1252 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435297 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1241} "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 {#1242} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1243} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1244} "content" => Illuminate\Database\Eloquent\Collection {#1246} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1252 …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 => "*" ] } 3 => App\Models\Task {#1247 #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" => 1435298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1245 …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 {#1254 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1250 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1264 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435298 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1245 …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 {#1254 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1250 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1248 …2} "content" => Illuminate\Database\Eloquent\Collection {#1249 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1264 …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" => 1435678 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-43" "field_display_title" => "43" "field_folder" => "3" "field_image_name" => "43" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1087} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1091} "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 {#1089} "content" => Illuminate\Database\Eloquent\Collection {#1115} "next" => array:2 [ "refs" => "1435679" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435677" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1211} ] #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" => 1435296 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "43" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/47-10" "field_display_title" => "10" "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 {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1114} "content" => Illuminate\Database\Eloquent\Collection {#1038} "next" => array:2 [ "refs" => "1435297" "type" => "task" ] "previous" => array:2 [ "refs" => "1435295" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1109} "page" => array:2 [ "refs" => "1435678" "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 => "*" ] }
№10 (с. 43)
Условие. №10 (с. 43)
скриншот условия
10. На рис. 47 показаны главные оптические оси тонкой собирающей (а) и тонкой рассеивающей (б) линз. Точками обозначены главные фокусы $\text{F}$ этих линз. Цифрой $1'$ обозначены лучи света, выходящие из линз. Постройте ход этих лучей до их преломления в линзах.
а
б
Рис. 47
Решение. №10 (с. 43)
Для построения хода лучей до их преломления в линзах используется свойство побочных фокусов и принцип обратимости световых лучей. Любой пучок параллельных лучей, падающих на линзу, после преломления собирается в одной точке фокальной плоскости (для собирающей линзы) или расходится так, как будто вышел из одной точки фокальной плоскости (для рассеивающей линзы). Эта точка называется побочным фокусом. Луч, проходящий через оптический центр, не меняет своего направления и определяет, какому побочному фокусу соответствует данное направление параллельных лучей.
Для нахождения падающего луча по известному преломленному лучу необходимо выполнить обратное построение.
аВ случае с собирающей линзой, все лучи, параллельные некоторому направлению, после преломления собираются в одной точке (побочном фокусе), лежащей в задней фокальной плоскости (плоскости, проходящей через задний фокус F перпендикулярно главной оптической оси).
1. Найдём точку F' — пересечение преломлённого луча 1' с задней фокальной плоскостью. Это и есть побочный фокус.
2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.
3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.
Ответ: Построение падающего луча показано на рисунке.
бВ случае с рассеивающей линзой, продолжения всех преломлённых лучей, соответствующих параллельному пучку падающих лучей, пересекаются в одной точке (мнимом побочном фокусе), лежащей в передней фокальной плоскости (плоскости, проходящей через передний фокус F).
1. Найдём точку F' — пересечение продолжения преломлённого луча 1' с передней фокальной плоскостью. Это мнимый побочный фокус.
2. Падающий луч должен быть параллелен побочной оптической оси, проходящей через оптический центр линзы O и побочный фокус F'.
3. Проведём через точку падения луча 1' на линзу искомый падающий луч 1, параллельно прямой OF'.
Ответ: Построение падающего луча показано на рисунке.
Другие задания:
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