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Номер 9, страница 48, 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 48. Построение изображений, создаваемых тонкими собирающими линзами - номер 9, страница 48.
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" => 1435313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-9" "field_display_title" => "9" "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" => 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 {#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" => 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 {#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" => 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 {#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" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "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 [ …6] "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 {#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" => 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 {#1040 #items: array:4 [ 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" => 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 {#1042 #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 {#1043 #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 {#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: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 {#1045 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046 #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: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 [ …6] "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 [ …6] "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 {#1048 #items: array:1 [ 0 => App\Models\Term {#1049 #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 {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #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 {#1052 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1053 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055 #items: array:1 [ 0 => App\Models\Term {#1056 #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" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057 #items: array:1 [ 0 => 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:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059 #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 {#1060 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063 #items: array:1 [ 0 => App\Models\Term {#1064 #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" => 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 {#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 {#1045} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1046} "field_country" => Illuminate\Database\Eloquent\Collection {#1048} "field_city" => Illuminate\Database\Eloquent\Collection {#1050} "field_series" => Illuminate\Database\Eloquent\Collection {#1052} "field_umk" => Illuminate\Database\Eloquent\Collection {#1053} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1054} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1055} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1057} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1059} "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 {#1060} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1061} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1062} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1063} "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 {#1065 #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 {#333} "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1065} ] #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 {#1066 #items: array:3 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1067 #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 {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 #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" …3 ] "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 {#1070 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Branch {#1072 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 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 {#1073 …2} "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 {#1074 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 …2} ] #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 {#1073 …2} "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 {#1074 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1075 …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" => 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 {#1068} "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 {#1070} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1071} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1076 #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" => 1434862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими собирающими линзами" "field_branch_order" => "48" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\Term {#1078 #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" => "45" "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 {#1079 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1080 #items: array:1 [ 0 => App\Models\Branch {#1081 #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 {#1082 …2} "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 {#1084 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1117 …2} ] #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 {#1082 …2} "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 {#1084 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1117 …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" => 1434862 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими собирающими линзами" "field_branch_order" => "48" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1077} "field_page_start" => "45" "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 {#1079} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1080} ] #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 {#1123 #items: array:2 [ 0 => App\Models\Element {#1124 #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" => 1698701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\Edition {#1126 #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 {#1127 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …2} "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 {#1127 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1129 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …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" => "1435313" "type" => "task" ] "text" => "<p><strong>9.</strong> На рис. 58 показан один из лучей, идущий от точечного источника света $\text{S}$ и проходящий через тонкую собирающую линзу. Штрихпунктирной линией показана главная оптическая ось $\text{AB}$ этой линзы. Укажите на рисунке положения главной и фокальных плоскостей линзы, а также положение изображения $S'$ источника.</p><p>Рис. 58</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1898" "height" => 741 "path" => "/media/fizika_09/grachev-rt/0-48/9-1.webp?ts=1759402878" ] ] ] #original: array:7 [ "id" => 1698701 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1125} "task" => array:2 [ "refs" => "1435313" "type" => "task" ] "text" => "<p><strong>9.</strong> На рис. 58 показан один из лучей, идущий от точечного источника света $\text{S}$ и проходящий через тонкую собирающую линзу. Штрихпунктирной линией показана главная оптическая ось $\text{AB}$ этой линзы. Укажите на рисунке положения главной и фокальных плоскостей линзы, а также положение изображения $S'$ источника.</p><p>Рис. 58</p>" "img" => array:1 [ 0 => array:5 [ "name" => "9-1.jpg" "alt" => null "width" => "1898" "height" => 741 "path" => "/media/fizika_09/grachev-rt/0-48/9-1.webp?ts=1759402878" ] ] ] #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 {#1132 #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" => 1734687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1133 #items: array:1 [ 0 => App\Models\Edition {#1134 #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 {#1135 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2} "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 {#1135 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …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" => "1435313" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для определения положения главной и фокальных плоскостей линзы, а также положения изображения S' источника S, воспользуемся правилами построения лучей в тонкой собирающей линзе. Построение будем производить в несколько этапов.</p><p><strong>1. Определение положения главной плоскости и оптического центра линзы.</strong></p><p>Главная плоскость тонкой линзы — это плоскость, в которой условно происходит преломление всех лучей. Чтобы найти её положение, нужно найти точку, в которой падающий луч "изламывается", превращаясь в преломлённый. Проведём через эту точку прямую, перпендикулярную главной оптической оси АВ. Эта прямая и будет являться главной плоскостью линзы. Точку пересечения главной плоскости с главной оптической осью называют оптическим центром линзы и обозначают буквой O.</p><p><strong>2. Определение положения фокусов и фокальных плоскостей линзы.</strong></p><p>Согласно правилу построения лучей, луч, падающий на собирающую линзу параллельно её главной оптической оси, после преломления проходит через главный (задний) фокус линзы F'. В задаче показан именно такой луч, идущий от источника S. Следовательно, точка, в которой преломлённый луч пересекает главную оптическую ось, и есть задний фокус F'. Плоскость, проходящая через фокус перпендикулярно главной оптической оси, называется фокальной плоскостью. Таким образом, мы находим заднюю фокальную плоскость.</p><p>Передний фокус F находится на главной оптической оси симметрично заднему фокусу F' относительно главной плоскости линзы. Это значит, что расстояние от оптического центра О до переднего фокуса F равно фокусному расстоянию, т.е. расстоянию от O до заднего фокуса F' ($OF = OF'$). Через точку F, перпендикулярно главной оптической оси, проходит передняя фокальная плоскость.</p><p><strong>3. Построение изображения S' источника S.</strong></p><p>Для построения изображения точки S необходимо найти точку пересечения как минимум двух лучей, вышедших из S и прошедших через линзу. Один преломлённый луч нам уже дан.</p><p>В качестве второго луча удобно использовать луч, идущий от источника S через оптический центр линзы O. Такой луч, проходя через тонкую линзу, не меняет своего направления.</p><p>Проведём прямую линию из точки S через оптический центр O. Точка пересечения этой прямой с уже имеющимся преломлённым лучом и будет являться действительным изображением источника S', которое даёт линза.</p><p>Итоговое построение показано на рисунке ниже.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе"></p><p><strong>Ответ:</strong> Положения главной и фокальных плоскостей, а также положение изображения S' показаны на рисунке. Главная плоскость проходит через точку излома луча перпендикулярно оптической оси. Задний фокус F' находится в точке пересечения преломлённого луча с оптической осью. Передний фокус F находится на том же расстоянии от главной плоскости, что и задний, но с противоположной стороны. Изображение S' находится на пересечении преломлённого луча (данного в условии) и луча, проведённого из источника S через оптический центр линзы O.</p>" ] #original: array:6 [ "id" => 1734687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1133} "task" => array:2 [ "refs" => "1435313" "type" => "task" ] "text" => "<p><strong>Решение</strong></p><p>Для определения положения главной и фокальных плоскостей линзы, а также положения изображения S' источника S, воспользуемся правилами построения лучей в тонкой собирающей линзе. Построение будем производить в несколько этапов.</p><p><strong>1. Определение положения главной плоскости и оптического центра линзы.</strong></p><p>Главная плоскость тонкой линзы — это плоскость, в которой условно происходит преломление всех лучей. Чтобы найти её положение, нужно найти точку, в которой падающий луч "изламывается", превращаясь в преломлённый. Проведём через эту точку прямую, перпендикулярную главной оптической оси АВ. Эта прямая и будет являться главной плоскостью линзы. Точку пересечения главной плоскости с главной оптической осью называют оптическим центром линзы и обозначают буквой O.</p><p><strong>2. Определение положения фокусов и фокальных плоскостей линзы.</strong></p><p>Согласно правилу построения лучей, луч, падающий на собирающую линзу параллельно её главной оптической оси, после преломления проходит через главный (задний) фокус линзы F'. В задаче показан именно такой луч, идущий от источника S. Следовательно, точка, в которой преломлённый луч пересекает главную оптическую ось, и есть задний фокус F'. Плоскость, проходящая через фокус перпендикулярно главной оптической оси, называется фокальной плоскостью. Таким образом, мы находим заднюю фокальную плоскость.</p><p>Передний фокус F находится на главной оптической оси симметрично заднему фокусу F' относительно главной плоскости линзы. Это значит, что расстояние от оптического центра О до переднего фокуса F равно фокусному расстоянию, т.е. расстоянию от O до заднего фокуса F' ($OF = OF'$). Через точку F, перпендикулярно главной оптической оси, проходит передняя фокальная плоскость.</p><p><strong>3. Построение изображения S' источника S.</strong></p><p>Для построения изображения точки S необходимо найти точку пересечения как минимум двух лучей, вышедших из S и прошедших через линзу. Один преломлённый луч нам уже дан.</p><p>В качестве второго луча удобно использовать луч, идущий от источника S через оптический центр линзы O. Такой луч, проходя через тонкую линзу, не меняет своего направления.</p><p>Проведём прямую линию из точки S через оптический центр O. Точка пересечения этой прямой с уже имеющимся преломлённым лучом и будет являться действительным изображением источника S', которое даёт линза.</p><p>Итоговое построение показано на рисунке ниже.</p><p><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе"></p><p><strong>Ответ:</strong> Положения главной и фокальных плоскостей, а также положение изображения S' показаны на рисунке. Главная плоскость проходит через точку излома луча перпендикулярно оптической оси. Задний фокус F' находится в точке пересечения преломлённого луча с оптической осью. Передний фокус F находится на том же расстоянии от главной плоскости, что и задний, но с противоположной стороны. Изображение S' находится на пересечении преломлённого луча (данного в условии) и луча, проведённого из источника S через оптический центр линзы O.</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" => "1435314" "type" => "task" ] "previous" => array:2 [ "refs" => "1435312" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Book {#1032} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\BookPage {#1154 #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" => 1435683 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-48" "field_display_title" => "48" "field_folder" => "3" "field_image_name" => "48" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Branch {#1156 #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 {#1158 …2} "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 {#1159 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1192 …2} ] #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 {#1158 …2} "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 {#1159 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1192 …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 } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1228 #items: array:1 [ 0 => App\Models\Book {#1193 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 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 {#1196 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1220 …2} "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 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1222 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1223 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1224 …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" => 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 {#1196 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1209 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1211 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1213 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1214 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1215 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1216 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1218 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1220 …2} "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 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1221 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1222 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1223 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1224 …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 {#1226 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1237 #items: array:1 [ 0 => App\Models\Element {#1236 #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" => 1699070 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1246 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1699070 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1246 …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" => "1435684" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435682" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1739 #items: array:4 [ 0 => App\Models\Task {#1229 #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" => 1435312 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1227 …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 {#1233 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1231 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1280 …2} "content" => 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{#1370 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1387 …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 {#1388 #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" => 1435313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1389 …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 {#1391 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1392 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1430 …2} "content" => Illuminate\Database\Eloquent\Collection {#1487 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1504 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection 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array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1621 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435314 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1506 …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 {#1508 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1509 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1547 …2} "content" => Illuminate\Database\Eloquent\Collection {#1604 …2} "next" => array:2 [ …2] "previous" => array:2 [ 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#hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1435313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "48" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/48-9" "field_display_title" => "9" "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 {#1066} "content" => Illuminate\Database\Eloquent\Collection {#1123} "next" => array:2 [ "refs" => "1435314" "type" => "task" ] "previous" => array:2 [ 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№9 (с. 48)
Условие. №9 (с. 48)
скриншот условия
9. На рис. 58 показан один из лучей, идущий от точечного источника света $\text{S}$ и проходящий через тонкую собирающую линзу. Штрихпунктирной линией показана главная оптическая ось $\text{AB}$ этой линзы. Укажите на рисунке положения главной и фокальных плоскостей линзы, а также положение изображения $S'$ источника.
Рис. 58
Решение. №9 (с. 48)
Решение
Для определения положения главной и фокальных плоскостей линзы, а также положения изображения S' источника S, воспользуемся правилами построения лучей в тонкой собирающей линзе. Построение будем производить в несколько этапов.
1. Определение положения главной плоскости и оптического центра линзы.
Главная плоскость тонкой линзы — это плоскость, в которой условно происходит преломление всех лучей. Чтобы найти её положение, нужно найти точку, в которой падающий луч "изламывается", превращаясь в преломлённый. Проведём через эту точку прямую, перпендикулярную главной оптической оси АВ. Эта прямая и будет являться главной плоскостью линзы. Точку пересечения главной плоскости с главной оптической осью называют оптическим центром линзы и обозначают буквой O.
2. Определение положения фокусов и фокальных плоскостей линзы.
Согласно правилу построения лучей, луч, падающий на собирающую линзу параллельно её главной оптической оси, после преломления проходит через главный (задний) фокус линзы F'. В задаче показан именно такой луч, идущий от источника S. Следовательно, точка, в которой преломлённый луч пересекает главную оптическую ось, и есть задний фокус F'. Плоскость, проходящая через фокус перпендикулярно главной оптической оси, называется фокальной плоскостью. Таким образом, мы находим заднюю фокальную плоскость.
Передний фокус F находится на главной оптической оси симметрично заднему фокусу F' относительно главной плоскости линзы. Это значит, что расстояние от оптического центра О до переднего фокуса F равно фокусному расстоянию, т.е. расстоянию от O до заднего фокуса F' ($OF = OF'$). Через точку F, перпендикулярно главной оптической оси, проходит передняя фокальная плоскость.
3. Построение изображения S' источника S.
Для построения изображения точки S необходимо найти точку пересечения как минимум двух лучей, вышедших из S и прошедших через линзу. Один преломлённый луч нам уже дан.
В качестве второго луча удобно использовать луч, идущий от источника S через оптический центр линзы O. Такой луч, проходя через тонкую линзу, не меняет своего направления.
Проведём прямую линию из точки S через оптический центр O. Точка пересечения этой прямой с уже имеющимся преломлённым лучом и будет являться действительным изображением источника S', которое даёт линза.
Итоговое построение показано на рисунке ниже.
Ответ: Положения главной и фокальных плоскостей, а также положение изображения S' показаны на рисунке. Главная плоскость проходит через точку излома луча перпендикулярно оптической оси. Задний фокус F' находится в точке пересечения преломлённого луча с оптической осью. Передний фокус F находится на том же расстоянии от главной плоскости, что и задний, но с противоположной стороны. Изображение S' находится на пересечении преломлённого луча (данного в условии) и луча, проведённого из источника S через оптический центр линзы O.
Другие задания:
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