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Номер 11, страница 237 - гдз по физике 8 класс учебник Изергин
Авторы: Изергин Э. Т.
Тип: Учебник
Издательство: Русское слово
Год издания: 2019 - 2026
Цвет обложки: синий
ISBN: 978-5-533-01067-2
Популярные ГДЗ в 8 классе
Глава V. Геометрическая оптика. Параграф 42. Линзы - номер 11, страница 237.
App\Models\Task {#1024 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1492591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1492199 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая оптика" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "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 [ …6] "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" => "211" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 4168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:1 [ 0 => App\Models\Term {#1035 #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 {#1036 #items: array:1 [ 0 => App\Models\Term {#1037 #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" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ …6] "field_translit" => "vosmoj" ] #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 {#1038 #items: array:1 [ 0 => App\Models\Term {#1039 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5176 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Русское слово" "field_cases" => null "field_translit" => "russkoe slovo" ] #original: array:6 [ "id" => 5176 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Русское слово" "field_cases" => null "field_translit" => "russkoe slovo" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4491 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Изергин" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Эдуард" "field_patronymic" => "Тимофеевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\Term {#1044 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ 0 => App\Models\Term {#1046 #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 {#1047 #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: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 {#1049 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => 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: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" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" "alt" => "" "width" => "1608" "height" => "2576" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #items: array:1 [ 0 => 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:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "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 [ …6] "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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 4168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043} "field_country" => Illuminate\Database\Eloquent\Collection {#1045} "field_city" => Illuminate\Database\Eloquent\Collection {#1047} "field_series" => Illuminate\Database\Eloquent\Collection {#1049} "field_umk" => Illuminate\Database\Eloquent\Collection {#1050} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" "alt" => "" "width" => "1608" "height" => "2576" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #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 {#1061 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1492199 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая оптика" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "211" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1061} ] #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 {#1062 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1063 #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" => 1492204 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линзы" "field_branch_order" => "42" "field_url" => null "field_branch_type" => 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:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "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 [ …6] "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" => "231" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067 #items: array:1 [ 0 => App\Models\Branch {#1068 #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" => 1492199 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая оптика" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_page_start" => "211" "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 {#1071 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1100 …2} ] #original: array:24 [ "id" => 1492199 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Геометрическая оптика" "field_branch_order" => "V" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_page_start" => "211" "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 {#1071 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1100 …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" => 1492204 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Линзы" "field_branch_order" => "42" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_page_start" => "231" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1067} ] #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 {#1101 #items: array:2 [ 0 => App\Models\Element {#1102 #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" => 1774734 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1103 #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" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1109 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1105 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1107 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1108 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1109 …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" => "1492591" "type" => "task" ] "text" => "<p><strong>11.</strong> Покажите дальнейший ход луча $AB$ (рис. 235).</p><p>Рис. 235. К заданию 11</p>" "img" => array:2 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "913" "height" => 195 "path" => "/media/fizika_08/izergin-u/0-42/11-1.webp?ts=1761329271" ] 1 => array:5 [ "name" => "11-2.jpg" "alt" => null "width" => "699" "height" => 675 "path" => "/media/fizika_08/izergin-u/0-42/11-2.webp?ts=1761329271" ] ] ] #original: array:7 [ "id" => 1774734 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1103} "task" => array:2 [ "refs" => "1492591" "type" => "task" ] "text" => "<p><strong>11.</strong> Покажите дальнейший ход луча $AB$ (рис. 235).</p><p>Рис. 235. К заданию 11</p>" "img" => array:2 [ 0 => array:5 [ "name" => "11-1.jpg" "alt" => null "width" => "913" "height" => 195 "path" => "/media/fizika_08/izergin-u/0-42/11-1.webp?ts=1761329271" ] 1 => array:5 [ "name" => "11-2.jpg" "alt" => null "width" => "699" "height" => 675 "path" => "/media/fizika_08/izergin-u/0-42/11-2.webp?ts=1761329271" ] ] ] #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 {#1110 #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" => 1851906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Edition {#1112 #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" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1117 …2} "field_content_source" => null ] #original: array:21 [ "id" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1113 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1115 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1116 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1117 …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" => "1492591" "type" => "task" ] "text" => "<p>На рисунке изображена рассеивающая линза, что следует из того, как расходятся лучи, изначально параллельные главной оптической оси. Чтобы определить дальнейший ход луча AB, исходящего из точки A, необходимо построить изображение этой точки, которое в рассеивающей линзе всегда является мнимым.</p><p>Построение выполняется в несколько этапов:</p><p><strong>1.</strong> <strong>Определение фокуса линзы (F).</strong> На рисунке показаны преломленные синие лучи, которые изначально были параллельны главной оптической оси. Если их продолжить в обратном направлении (влево от линзы), они пересекутся в одной точке на главной оптической оси. Эта точка является передним главным фокусом линзы F.</p><p><strong>2.</strong> <strong>Построение мнимого изображения A' точки A.</strong> Для этого необходимо использовать как минимум два луча, исходящих из точки A, дальнейший ход которых известен:</p><p>- Первый луч, направленный из точки A параллельно главной оптической оси. После преломления в линзе он пойдет так, что его продолжение в обратную сторону пройдет через фокус F.</p><p>- Второй луч, направленный из точки A через оптический центр линзы. Этот луч проходит через линзу, не изменяя своего направления.</p><p>Точка пересечения продолжения первого преломленного луча и второго луча (который не преломился) дает нам положение мнимого изображения A'.</p><p><strong>3.</strong> <strong>Определение дальнейшего хода луча AB.</strong> Согласно законам геометрической оптики, все лучи, вышедшие из точки A, после преломления в линзе будут расходиться так, как будто они исходят из точки мнимого изображения A'. Следовательно, луч AB после преломления в точке B пойдет по прямой, которая является продолжением линии, соединяющей точки A' и B.</p><p>Таким образом, для графического решения задачи нужно соединить прямой линией найденную точку A' и точку B и продолжить эту прямую вправо от линзы. Этот продолженный отрезок и будет искомым преломленным лучом.</p><p><strong>Ответ:</strong> Дальнейший ход луча AB — это луч, выходящий из точки B в таком направлении, что его продолжение в обратную сторону проходит через точку мнимого изображения A' источника света A.</p>" ] #original: array:6 [ "id" => 1851906 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1111} "task" => array:2 [ "refs" => "1492591" "type" => "task" ] "text" => "<p>На рисунке изображена рассеивающая линза, что следует из того, как расходятся лучи, изначально параллельные главной оптической оси. Чтобы определить дальнейший ход луча AB, исходящего из точки A, необходимо построить изображение этой точки, которое в рассеивающей линзе всегда является мнимым.</p><p>Построение выполняется в несколько этапов:</p><p><strong>1.</strong> <strong>Определение фокуса линзы (F).</strong> На рисунке показаны преломленные синие лучи, которые изначально были параллельны главной оптической оси. Если их продолжить в обратном направлении (влево от линзы), они пересекутся в одной точке на главной оптической оси. Эта точка является передним главным фокусом линзы F.</p><p><strong>2.</strong> <strong>Построение мнимого изображения A' точки A.</strong> Для этого необходимо использовать как минимум два луча, исходящих из точки A, дальнейший ход которых известен:</p><p>- Первый луч, направленный из точки A параллельно главной оптической оси. После преломления в линзе он пойдет так, что его продолжение в обратную сторону пройдет через фокус F.</p><p>- Второй луч, направленный из точки A через оптический центр линзы. Этот луч проходит через линзу, не изменяя своего направления.</p><p>Точка пересечения продолжения первого преломленного луча и второго луча (который не преломился) дает нам положение мнимого изображения A'.</p><p><strong>3.</strong> <strong>Определение дальнейшего хода луча AB.</strong> Согласно законам геометрической оптики, все лучи, вышедшие из точки A, после преломления в линзе будут расходиться так, как будто они исходят из точки мнимого изображения A'. Следовательно, луч AB после преломления в точке B пойдет по прямой, которая является продолжением линии, соединяющей точки A' и B.</p><p>Таким образом, для графического решения задачи нужно соединить прямой линией найденную точку A' и точку B и продолжить эту прямую вправо от линзы. Этот продолженный отрезок и будет искомым преломленным лучом.</p><p><strong>Ответ:</strong> Дальнейший ход луча AB — это луч, выходящий из точки B в таком направлении, что его продолжение в обратную сторону проходит через точку мнимого изображения A' источника света A.</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" => "1492592" "type" => "task" ] "previous" => array:2 [ "refs" => "1492590" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1339 #items: array:1 [ 0 => App\Models\BookPage {#1123 #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" => 1492129 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_url" => "/8-klass/fizika/izergin-uchebnik/page-237" "field_display_title" => "237" "field_folder" => "1" "field_image_name" => "237" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1126 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Book {#1127 #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" => 4168 "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 {#1128 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1151 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 4168 "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 {#1128 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1134 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1146 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1148 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1149 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1150 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1151 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1152 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1153 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "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 {#1155 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1156 #items: array:1 [ 0 => App\Models\Element {#1157 #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" => 1775030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1158 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1775030 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1158 …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" => "1492130" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1492128" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:11 [ 0 => App\Models\Task {#1166 #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" => 1492581 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1169 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1170 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1176 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1226 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492581 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1167 …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 {#1169 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1170 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1176 …2} "content" => Illuminate\Database\Eloquent\Collection {#1215 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1226 …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 => "*" ] } 1 => App\Models\Task {#1227 #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" => 1492582 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228 …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 {#1229 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231 …2} "content" => Illuminate\Database\Eloquent\Collection {#1232 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1237 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492582 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1228 …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 {#1229 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1230 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231 …2} "content" => Illuminate\Database\Eloquent\Collection {#1232 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1237 …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 => "*" ] } 2 => App\Models\Task {#1238 #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" => 1492583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 …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 {#1240 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1241 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242 …2} "content" => Illuminate\Database\Eloquent\Collection {#1243 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1248 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492583 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1239 …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 {#1240 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1241 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1242 …2} "content" => Illuminate\Database\Eloquent\Collection {#1243 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1248 …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 {#1249 #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" => 1492584 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250 …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 {#1251 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1252 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253 …2} "content" => Illuminate\Database\Eloquent\Collection {#1254 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1259 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492584 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1250 …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 {#1251 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1252 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1253 …2} "content" => Illuminate\Database\Eloquent\Collection {#1254 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1259 …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 => "*" ] } 4 => App\Models\Task {#1260 #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" => 1492585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1262 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2} "content" => Illuminate\Database\Eloquent\Collection {#1265 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1270 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492585 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1261 …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 {#1262 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1263 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1264 …2} "content" => Illuminate\Database\Eloquent\Collection {#1265 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1270 …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 => "*" ] } 5 => App\Models\Task {#1271 #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" => 1492586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272 …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 {#1273 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275 …2} "content" => Illuminate\Database\Eloquent\Collection {#1276 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1281 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492586 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1272 …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 {#1273 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1274 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1275 …2} "content" => Illuminate\Database\Eloquent\Collection {#1276 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1281 …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 => "*" ] } 6 => App\Models\Task {#1282 #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" => 1492587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1283 …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 {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1285 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1286 …2} "content" => Illuminate\Database\Eloquent\Collection {#1287 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1292 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492587 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1283 …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 {#1284 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1285 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1286 …2} "content" => Illuminate\Database\Eloquent\Collection {#1287 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1292 …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 => "*" ] } 7 => App\Models\Task {#1293 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1492588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 …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 {#1295 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492588 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1294 …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 {#1295 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1296 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1297 …2} "content" => Illuminate\Database\Eloquent\Collection {#1298 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1303 …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 => "*" ] } 8 => App\Models\Task {#1304 #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" => 1492589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1305 …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 {#1306 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1308 …2} "content" => Illuminate\Database\Eloquent\Collection {#1309 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1314 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492589 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1305 …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 {#1306 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1307 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1308 …2} "content" => Illuminate\Database\Eloquent\Collection {#1309 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1314 …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 => "*" ] } 9 => App\Models\Task {#1315 #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" => 1492590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1316 …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 {#1317 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1318 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1319 …2} "content" => Illuminate\Database\Eloquent\Collection {#1320 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1325 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492590 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1316 …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 {#1317 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1318 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1319 …2} "content" => Illuminate\Database\Eloquent\Collection {#1320 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1325 …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 => "*" ] } 10 => App\Models\Task {#1326 #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" => 1492591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1327 …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 {#1328 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1329 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1330 …2} "content" => Illuminate\Database\Eloquent\Collection {#1331 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1336 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-11" "field_display_title" => "11" …17 ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1492129 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_url" => "/8-klass/fizika/izergin-uchebnik/page-237" "field_display_title" => "237" "field_folder" => "1" "field_image_name" => "237" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1126} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1125} "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 {#1155} "content" => Illuminate\Database\Eloquent\Collection {#1156} "next" => array:2 [ "refs" => "1492130" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1492128" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1165} ] #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" => 1492591 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "237" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/42-11" "field_display_title" => "11" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1026} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1062} "content" => Illuminate\Database\Eloquent\Collection {#1101} "next" => array:2 [ "refs" => "1492592" "type" => "task" ] "previous" => array:2 [ "refs" => "1492590" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1118} "page" => array:2 [ "refs" => "1492129" "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 => "*" ] }
№11 (с. 237)
Условие. №11 (с. 237)
скриншот условия
11. Покажите дальнейший ход луча $AB$ (рис. 235).
Рис. 235. К заданию 11
Решение. №11 (с. 237)
На рисунке изображена рассеивающая линза, что следует из того, как расходятся лучи, изначально параллельные главной оптической оси. Чтобы определить дальнейший ход луча AB, исходящего из точки A, необходимо построить изображение этой точки, которое в рассеивающей линзе всегда является мнимым.
Построение выполняется в несколько этапов:
1. Определение фокуса линзы (F). На рисунке показаны преломленные синие лучи, которые изначально были параллельны главной оптической оси. Если их продолжить в обратном направлении (влево от линзы), они пересекутся в одной точке на главной оптической оси. Эта точка является передним главным фокусом линзы F.
2. Построение мнимого изображения A' точки A. Для этого необходимо использовать как минимум два луча, исходящих из точки A, дальнейший ход которых известен:
- Первый луч, направленный из точки A параллельно главной оптической оси. После преломления в линзе он пойдет так, что его продолжение в обратную сторону пройдет через фокус F.
- Второй луч, направленный из точки A через оптический центр линзы. Этот луч проходит через линзу, не изменяя своего направления.
Точка пересечения продолжения первого преломленного луча и второго луча (который не преломился) дает нам положение мнимого изображения A'.
3. Определение дальнейшего хода луча AB. Согласно законам геометрической оптики, все лучи, вышедшие из точки A, после преломления в линзе будут расходиться так, как будто они исходят из точки мнимого изображения A'. Следовательно, луч AB после преломления в точке B пойдет по прямой, которая является продолжением линии, соединяющей точки A' и B.
Таким образом, для графического решения задачи нужно соединить прямой линией найденную точку A' и точку B и продолжить эту прямую вправо от линзы. Этот продолженный отрезок и будет искомым преломленным лучом.
Ответ: Дальнейший ход луча AB — это луч, выходящий из точки B в таком направлении, что его продолжение в обратную сторону проходит через точку мнимого изображения A' источника света A.
Другие задания:
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