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Номер 6, страница 52, 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 49. Построение изображений, создаваемых тонкими рассеивающими линзами - номер 6, страница 52.
App\Models\Task {#1030 // resources/views/models/task/default.blade.php #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1435328 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037 #items: array:1 [ 0 => App\Models\Term {#1036 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #original: array:6 [ "id" => 26 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "номер" "field_cases" => array:6 [ "field_accusative_case" => "номер" "field_creative_case" => "номером" "field_dative_case" => "номеру" "field_genitive_case" => "номера" "field_nominative_case" => "номер" "field_prepositional_case" => "номере" ] "field_short_name" => "№" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:1 [ 0 => App\Models\Branch {#1045 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1047 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ "field_accusative_case" => "Часть" "field_creative_case" => "Частью" "field_dative_case" => "Части" "field_genitive_case" => "Части" "field_nominative_case" => "Часть" "field_prepositional_case" => "Части" ] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083 #items: array:1 [ 0 => App\Models\Book {#1049 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051 #items: array:1 [ 0 => App\Models\Term {#1048 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ "field_accusative_case" => "физику" "field_creative_case" => "физикой" "field_dative_case" => "физике" "field_genitive_case" => "физики" "field_nominative_case" => "физика" "field_prepositional_case" => "физике" ] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ 0 => App\Models\Term {#1053 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ "field_accusative_case" => "девятый" "field_creative_case" => "девятым" "field_dative_case" => "девятому" "field_genitive_case" => "девятого" "field_nominative_case" => "девятый" "field_prepositional_case" => "девятом" ] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054 #items: array:1 [ 0 => App\Models\Term {#1055 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #original: array:6 [ "id" => 5153 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Просвещение" "field_cases" => null "field_translit" => "prosveschenie" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1056 #items: array:4 [ 0 => App\Models\Term {#1057 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1058 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1059 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1060 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "рабочую тетрадь" "field_creative_case" => "рабочей тетрадью" "field_dative_case" => "рабочей тетради" "field_genitive_case" => "рабочей тетради" "field_nominative_case" => "рабочая тетрадь" "field_prepositional_case" => "рабочей тетради" ] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1066 #items: array:1 [ 0 => App\Models\Term {#1067 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1068 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1069 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: array:1 [ 0 => App\Models\Term {#1072 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Term {#1074 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079 #items: array:1 [ 0 => App\Models\Term {#1080 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ "field_accusative_case" => null "field_creative_case" => null "field_dative_case" => null "field_genitive_case" => null "field_nominative_case" => null "field_prepositional_case" => null ] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1051} "field_class" => Illuminate\Database\Eloquent\Collection {#1052} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1054} "field_author" => Illuminate\Database\Eloquent\Collection {#1056} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1061} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_country" => Illuminate\Database\Eloquent\Collection {#1064} "field_city" => Illuminate\Database\Eloquent\Collection {#1066} "field_series" => Illuminate\Database\Eloquent\Collection {#1068} "field_umk" => Illuminate\Database\Eloquent\Collection {#1069} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1070} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1073} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1076} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1077} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1078} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1079} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1083} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1188 #items: array:3 [ 0 => App\Models\Branch {#1198 #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 {#1199 #items: array:1 [ 0 => App\Models\Term {#1047} ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1200 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201 #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 {#1199} "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 {#1200} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1201} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Branch {#1202 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 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 {#1206 #items: array:1 [ 0 => App\Models\Term {#1203 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206} "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 {#1205} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204} ] #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 {#1207 #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" => 1434863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Term {#1208 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ "field_accusative_case" => "Параграф" "field_creative_case" => "Параграфом" "field_dative_case" => "Параграфу" "field_genitive_case" => "Параграфа" "field_nominative_case" => "Параграф" "field_prepositional_case" => "Параграфе" ] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "51" "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 {#1210 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1287 #items: array:1 [ 0 => App\Models\Branch {#1209 #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 {#1213 #items: array:1 [ 0 => App\Models\Term {#1212 #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 [ …7] #original: array:7 [ …7] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] …1 } ] #escapeWhenCastingToString: false } "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1214 #items: array:1 [ 0 => App\Models\Book {#1215 …30} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ 0 => App\Models\Branch {#1248 …30} ] #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 {#1213} "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 {#1214} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1247} ] #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" => 1434863 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1211} "field_page_start" => "51" "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 {#1210} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1287} ] #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 {#1113 #items: array:2 [ 0 => App\Models\Element {#1182 #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" => 1698716 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Edition {#1181 #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 {#1178 #items: array:1 [ 0 => App\Models\Term {#1180 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1179 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1178} "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 {#1179} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1176} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1177} "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" => "1435328" "type" => "task" ] "text" => "<p><strong>6.</strong> Точечный источник света находится на расстоянии $\text{a}$ от главной плоскости тонкой рассеивающей линзы с фокусным расстоянием $\text{F}$ и оптической силой $\text{D}$. Заполните таблицу, определив неизвестные величины. Здесь $\text{b}$ — расстояние от главной плоскости линзы до изображения источника.</p><div class="table-wrap"><table style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">№ линзы</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{F}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{D}$, дптр</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{a}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{b}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$(a+b)$, см</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">1</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-25$</td><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">2</td><td style="border: 1px solid rgb(0, 0, 0);">$-60$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">30</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">3</td><td style="border: 1px solid rgb(0, 0, 0);">$-20$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-40/3$</td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);">$-6$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-2$</td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">5*</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-50$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-0,5$</td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">6*</td><td style="border: 1px solid rgb(0, 0, 0);">$-3$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">4</td></tr></tbody></table></div>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1977" "height" => 964 "path" => "/media/fizika_09/grachev-rt/0-49/6-1.webp?ts=1759402878" ] ] ] #original: array:7 [ "id" => 1698716 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1173} "task" => array:2 [ "refs" => "1435328" "type" => "task" ] "text" => "<p><strong>6.</strong> Точечный источник света находится на расстоянии $\text{a}$ от главной плоскости тонкой рассеивающей линзы с фокусным расстоянием $\text{F}$ и оптической силой $\text{D}$. Заполните таблицу, определив неизвестные величины. Здесь $\text{b}$ — расстояние от главной плоскости линзы до изображения источника.</p><div class="table-wrap"><table style="border: 1px solid rgb(0, 0, 0);"><thead><tr><th style="border: 1px solid rgb(0, 0, 0);">№ линзы</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{F}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{D}$, дптр</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{a}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$\text{b}$, см</th><th style="border: 1px solid rgb(0, 0, 0);">$(a+b)$, см</th></tr></thead><tbody><tr><td style="border: 1px solid rgb(0, 0, 0);">1</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-25$</td><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">2</td><td style="border: 1px solid rgb(0, 0, 0);">$-60$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">30</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">3</td><td style="border: 1px solid rgb(0, 0, 0);">$-20$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-40/3$</td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">4</td><td style="border: 1px solid rgb(0, 0, 0);">$-6$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-2$</td><td style="border: 1px solid rgb(0, 0, 0);"></td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">5*</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-50$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">$-0,5$</td></tr><tr><td style="border: 1px solid rgb(0, 0, 0);">6*</td><td style="border: 1px solid rgb(0, 0, 0);">$-3$</td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);"></td><td style="border: 1px solid rgb(0, 0, 0);">4</td></tr></tbody></table></div>" "img" => array:1 [ 0 => array:5 [ "name" => "6-1.jpg" "alt" => null "width" => "1977" "height" => 964 "path" => "/media/fizika_09/grachev-rt/0-49/6-1.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 {#1175 #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" => 1734702 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1174 #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 {#1172 #items: array:1 [ 0 => App\Models\Term {#1171 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1169 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1170 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1172} "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 {#1169} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1170} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1167} "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" => "1435328" "type" => "task" ] "text" => "<p>Для решения задачи используются формула тонкой линзы и формула для оптической силы. Поскольку линза рассеивающая, ее фокусное расстояние $F$ и оптическая сила $D$ являются отрицательными величинами. Источник света считается действительным, поэтому расстояние до него $a$ всегда положительно. Для рассеивающей линзы изображение действительного источника всегда мнимое, поэтому расстояние до изображения $b$ будет отрицательным.</p><p>Основная формула тонкой линзы: $\frac{1}{a} + \frac{1}{b} = \frac{1}{F}$</p><p>Связь оптической силы $D$ (в диоптриях, дптр) и фокусного расстояния $F$ (в метрах, м): $D = \frac{1}{F}$</p><strong>1. Линза № 1</strong><p><strong>Дано:</strong></p><p>$D = -25$ дптр</p><p>$a = 4$ см</p><p>$a = 0.04$ м</p><p><strong>Найти:</strong></p><p>$F, b, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем фокусное расстояние $F$, используя значение оптической силы $D$. Фокусное расстояние должно быть выражено в метрах.</p><p>$F = \frac{1}{D} = \frac{1}{-25} = -0.04$ м.</p><p>Переведем $F$ в сантиметры: $F = -4$ см.</p><p>Теперь воспользуемся формулой тонкой линзы для нахождения $b$. Расчеты будем вести в сантиметрах.</p><p>$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-4} - \frac{1}{4} = -\frac{2}{4} = -\frac{1}{2}$ см$^{-1}$.</p><p>Отсюда $b = -2$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 4 \text{ см} + (-2 \text{ см}) = 2$ см.</p><p><strong>Ответ:</strong> $F = -4$ см; $b = -2$ см; $(a+b) = 2$ см.</p><strong>2. Линза № 2</strong><p><strong>Дано:</strong></p><p>$F = -60$ см</p><p>$a = 30$ см</p><p>$F = -0.6$ м</p><p>$a = 0.3$ м</p><p><strong>Найти:</strong></p><p>$D, b, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$. Для этого фокусное расстояние $F$ нужно перевести в метры: $F = -60$ см $= -0.6$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.6} = -\frac{10}{6} = -\frac{5}{3}$ дптр $\approx -1.67$ дптр.</p><p>Найдем расстояние до изображения $b$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-60} - \frac{1}{30} = -\frac{1}{60} - \frac{2}{60} = -\frac{3}{60} = -\frac{1}{20}$ см$^{-1}$.</p><p>Отсюда $b = -20$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 30 \text{ см} + (-20 \text{ см}) = 10$ см.</p><p><strong>Ответ:</strong> $D = -5/3$ дптр; $b = -20$ см; $(a+b) = 10$ см.</p><strong>3. Линза № 3</strong><p><strong>Дано:</strong></p><p>$F = -20$ см</p><p>$b = -40/3$ см</p><p>$F = -0.2$ м</p><p>$b \approx -0.133$ м</p><p><strong>Найти:</strong></p><p>$D, a, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -20$ см $= -0.2$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.2} = -5$ дптр.</p><p>Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-20} - \frac{1}{-40/3} = -\frac{1}{20} + \frac{3}{40} = -\frac{2}{40} + \frac{3}{40} = \frac{1}{40}$ см$^{-1}$.</p><p>Отсюда $a = 40$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 40 \text{ см} + (-\frac{40}{3} \text{ см}) = \frac{120-40}{3} = \frac{80}{3}$ см.</p><p><strong>Ответ:</strong> $D = -5$ дптр; $a = 40$ см; $(a+b) = 80/3$ см.</p><strong>4. Линза № 4</strong><p><strong>Дано:</strong></p><p>$F = -6$ см</p><p>$b = -2$ см</p><p>$F = -0.06$ м</p><p>$b = -0.02$ м</p><p><strong>Найти:</strong></p><p>$D, a, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -6$ см $= -0.06$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.06} = -\frac{100}{6} = -\frac{50}{3}$ дптр $\approx -16.67$ дптр.</p><p>Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-6} - \frac{1}{-2} = -\frac{1}{6} + \frac{1}{2} = -\frac{1}{6} + \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$ см$^{-1}$.</p><p>Отсюда $a = 3$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 3 \text{ см} + (-2 \text{ см}) = 1$ см.</p><p><strong>Ответ:</strong> $D = -50/3$ дптр; $a = 3$ см; $(a+b) = 1$ см.</p><strong>5. Линза № 5*</strong><p><strong>Дано:</strong></p><p>$D = -50$ дптр</p><p>$(a+b) = -0.5$ см</p><p>$(a+b) = -0.005$ м</p><p><strong>Найти:</strong></p><p>$F, a, b$</p><p><strong>Решение:</strong></p><p>Найдем фокусное расстояние $F$:</p><p>$F = \frac{1}{D} = \frac{1}{-50} = -0.02$ м $= -2$ см.</p><p>Для рассеивающей линзы и действительного источника ($a > 0$) изображение всегда мнимое ($b < 0$), причем по модулю расстояние до изображения меньше расстояния до источника ($|b| < a$).</p><p>Из условия $(a+b) = -0.5$ выразим $a$: $a = -0.5 - b$.</p><p>Проверим условие $a > 0$: $-0.5 - b > 0$, что означает $b < -0.5$ см.</p><p>Проверим условие $|b| < a$. Поскольку $b < 0$, то $|b| = -b$. Подставим в неравенство:</p><p>$-b < -0.5 - b \Rightarrow 0 < -0.5$.</p><p>Полученное неравенство ложно. Это означает, что исходные данные противоречат законам оптики и задача с такими данными не имеет физического решения. Вероятно, в условии допущена опечатка.</p><p>Предположим, что в условии имелось в виду $(a+b) = 0.5$ см. Решим задачу для этого случая.</p><p>Имеем систему уравнений:</p><p>1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-2}$</p><p>2) $a+b = 0.5 \Rightarrow a = 0.5 - b$</p><p>Подставим (2) в (1): $\frac{1}{0.5-b} + \frac{1}{b} = -\frac{1}{2}$.</p><p>Приведем к общему знаменателю: $\frac{b + 0.5 - b}{b(0.5-b)} = -\frac{1}{2} \Rightarrow \frac{0.5}{0.5b - b^2} = -\frac{1}{2}$.</p><p>Отсюда $1 = -(0.5b - b^2)$, что приводит к квадратному уравнению $b^2 - 0.5b - 1 = 0$.</p><p>Дискриминант $D_q = (-0.5)^2 - 4(1)(-1) = 0.25 + 4 = 4.25$.</p><p>Корни $b = \frac{0.5 \pm \sqrt{4.25}}{2}$. Так как $b<0$, выбираем корень со знаком минус:</p><p>$b = \frac{0.5 - \sqrt{4.25}}{2} = \frac{1 - \sqrt{17}}{4}$ см.</p><p>Тогда $a = 0.5 - b = \frac{1}{2} - \frac{1 - \sqrt{17}}{4} = \frac{2 - 1 + \sqrt{17}}{4} = \frac{1 + \sqrt{17}}{4}$ см.</p><p><strong>Ответ:</strong> Исходные данные противоречивы. При предположении, что $(a+b) = 0.5$ см, ответ: $F = -2$ см; $a = \frac{1 + \sqrt{17}}{4}$ см; $b = \frac{1 - \sqrt{17}}{4}$ см.</p><strong>6. Линза № 6*</strong><p><strong>Дано:</strong></p><p>$F = -3$ см</p><p>$(a+b) = 4$ см</p><p>$F = -0.03$ м</p><p>$(a+b) = 0.04$ м</p><p><strong>Найти:</strong></p><p>$D, a, b$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -3$ см $= -0.03$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.03} = -\frac{100}{3}$ дптр $\approx -33.33$ дптр.</p><p>Решим систему уравнений:</p><p>1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-3}$</p><p>2) $a+b = 4 \Rightarrow a = 4 - b$</p><p>Подставим (2) в (1): $\frac{1}{4-b} + \frac{1}{b} = -\frac{1}{3}$.</p><p>Приведем к общему знаменателю: $\frac{b + 4 - b}{b(4-b)} = -\frac{1}{3} \Rightarrow \frac{4}{4b-b^2} = -\frac{1}{3}$.</p><p>Отсюда $12 = -(4b-b^2)$, что приводит к квадратному уравнению $b^2 - 4b - 12 = 0$.</p><p>По теореме Виета, корни уравнения $b_1=6$ и $b_2=-2$.</p><p>Так как изображение мнимое, $b$ должно быть отрицательным. Следовательно, $b = -2$ см.</p><p>Найдем $a$: $a = 4 - b = 4 - (-2) = 6$ см.</p><p><strong>Ответ:</strong> $D = -100/3$ дптр; $a = 6$ см; $b = -2$ см.</p>" ] #original: array:6 [ "id" => 1734702 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "task" => array:2 [ "refs" => "1435328" "type" => "task" ] "text" => "<p>Для решения задачи используются формула тонкой линзы и формула для оптической силы. Поскольку линза рассеивающая, ее фокусное расстояние $F$ и оптическая сила $D$ являются отрицательными величинами. Источник света считается действительным, поэтому расстояние до него $a$ всегда положительно. Для рассеивающей линзы изображение действительного источника всегда мнимое, поэтому расстояние до изображения $b$ будет отрицательным.</p><p>Основная формула тонкой линзы: $\frac{1}{a} + \frac{1}{b} = \frac{1}{F}$</p><p>Связь оптической силы $D$ (в диоптриях, дптр) и фокусного расстояния $F$ (в метрах, м): $D = \frac{1}{F}$</p><strong>1. Линза № 1</strong><p><strong>Дано:</strong></p><p>$D = -25$ дптр</p><p>$a = 4$ см</p><p>$a = 0.04$ м</p><p><strong>Найти:</strong></p><p>$F, b, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем фокусное расстояние $F$, используя значение оптической силы $D$. Фокусное расстояние должно быть выражено в метрах.</p><p>$F = \frac{1}{D} = \frac{1}{-25} = -0.04$ м.</p><p>Переведем $F$ в сантиметры: $F = -4$ см.</p><p>Теперь воспользуемся формулой тонкой линзы для нахождения $b$. Расчеты будем вести в сантиметрах.</p><p>$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-4} - \frac{1}{4} = -\frac{2}{4} = -\frac{1}{2}$ см$^{-1}$.</p><p>Отсюда $b = -2$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 4 \text{ см} + (-2 \text{ см}) = 2$ см.</p><p><strong>Ответ:</strong> $F = -4$ см; $b = -2$ см; $(a+b) = 2$ см.</p><strong>2. Линза № 2</strong><p><strong>Дано:</strong></p><p>$F = -60$ см</p><p>$a = 30$ см</p><p>$F = -0.6$ м</p><p>$a = 0.3$ м</p><p><strong>Найти:</strong></p><p>$D, b, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$. Для этого фокусное расстояние $F$ нужно перевести в метры: $F = -60$ см $= -0.6$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.6} = -\frac{10}{6} = -\frac{5}{3}$ дптр $\approx -1.67$ дптр.</p><p>Найдем расстояние до изображения $b$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-60} - \frac{1}{30} = -\frac{1}{60} - \frac{2}{60} = -\frac{3}{60} = -\frac{1}{20}$ см$^{-1}$.</p><p>Отсюда $b = -20$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 30 \text{ см} + (-20 \text{ см}) = 10$ см.</p><p><strong>Ответ:</strong> $D = -5/3$ дптр; $b = -20$ см; $(a+b) = 10$ см.</p><strong>3. Линза № 3</strong><p><strong>Дано:</strong></p><p>$F = -20$ см</p><p>$b = -40/3$ см</p><p>$F = -0.2$ м</p><p>$b \approx -0.133$ м</p><p><strong>Найти:</strong></p><p>$D, a, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -20$ см $= -0.2$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.2} = -5$ дптр.</p><p>Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-20} - \frac{1}{-40/3} = -\frac{1}{20} + \frac{3}{40} = -\frac{2}{40} + \frac{3}{40} = \frac{1}{40}$ см$^{-1}$.</p><p>Отсюда $a = 40$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 40 \text{ см} + (-\frac{40}{3} \text{ см}) = \frac{120-40}{3} = \frac{80}{3}$ см.</p><p><strong>Ответ:</strong> $D = -5$ дптр; $a = 40$ см; $(a+b) = 80/3$ см.</p><strong>4. Линза № 4</strong><p><strong>Дано:</strong></p><p>$F = -6$ см</p><p>$b = -2$ см</p><p>$F = -0.06$ м</p><p>$b = -0.02$ м</p><p><strong>Найти:</strong></p><p>$D, a, (a+b)$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -6$ см $= -0.06$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.06} = -\frac{100}{6} = -\frac{50}{3}$ дптр $\approx -16.67$ дптр.</p><p>Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):</p><p>$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-6} - \frac{1}{-2} = -\frac{1}{6} + \frac{1}{2} = -\frac{1}{6} + \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$ см$^{-1}$.</p><p>Отсюда $a = 3$ см.</p><p>Вычислим сумму $(a+b)$:</p><p>$(a+b) = 3 \text{ см} + (-2 \text{ см}) = 1$ см.</p><p><strong>Ответ:</strong> $D = -50/3$ дптр; $a = 3$ см; $(a+b) = 1$ см.</p><strong>5. Линза № 5*</strong><p><strong>Дано:</strong></p><p>$D = -50$ дптр</p><p>$(a+b) = -0.5$ см</p><p>$(a+b) = -0.005$ м</p><p><strong>Найти:</strong></p><p>$F, a, b$</p><p><strong>Решение:</strong></p><p>Найдем фокусное расстояние $F$:</p><p>$F = \frac{1}{D} = \frac{1}{-50} = -0.02$ м $= -2$ см.</p><p>Для рассеивающей линзы и действительного источника ($a > 0$) изображение всегда мнимое ($b < 0$), причем по модулю расстояние до изображения меньше расстояния до источника ($|b| < a$).</p><p>Из условия $(a+b) = -0.5$ выразим $a$: $a = -0.5 - b$.</p><p>Проверим условие $a > 0$: $-0.5 - b > 0$, что означает $b < -0.5$ см.</p><p>Проверим условие $|b| < a$. Поскольку $b < 0$, то $|b| = -b$. Подставим в неравенство:</p><p>$-b < -0.5 - b \Rightarrow 0 < -0.5$.</p><p>Полученное неравенство ложно. Это означает, что исходные данные противоречат законам оптики и задача с такими данными не имеет физического решения. Вероятно, в условии допущена опечатка.</p><p>Предположим, что в условии имелось в виду $(a+b) = 0.5$ см. Решим задачу для этого случая.</p><p>Имеем систему уравнений:</p><p>1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-2}$</p><p>2) $a+b = 0.5 \Rightarrow a = 0.5 - b$</p><p>Подставим (2) в (1): $\frac{1}{0.5-b} + \frac{1}{b} = -\frac{1}{2}$.</p><p>Приведем к общему знаменателю: $\frac{b + 0.5 - b}{b(0.5-b)} = -\frac{1}{2} \Rightarrow \frac{0.5}{0.5b - b^2} = -\frac{1}{2}$.</p><p>Отсюда $1 = -(0.5b - b^2)$, что приводит к квадратному уравнению $b^2 - 0.5b - 1 = 0$.</p><p>Дискриминант $D_q = (-0.5)^2 - 4(1)(-1) = 0.25 + 4 = 4.25$.</p><p>Корни $b = \frac{0.5 \pm \sqrt{4.25}}{2}$. Так как $b<0$, выбираем корень со знаком минус:</p><p>$b = \frac{0.5 - \sqrt{4.25}}{2} = \frac{1 - \sqrt{17}}{4}$ см.</p><p>Тогда $a = 0.5 - b = \frac{1}{2} - \frac{1 - \sqrt{17}}{4} = \frac{2 - 1 + \sqrt{17}}{4} = \frac{1 + \sqrt{17}}{4}$ см.</p><p><strong>Ответ:</strong> Исходные данные противоречивы. При предположении, что $(a+b) = 0.5$ см, ответ: $F = -2$ см; $a = \frac{1 + \sqrt{17}}{4}$ см; $b = \frac{1 - \sqrt{17}}{4}$ см.</p><strong>6. Линза № 6*</strong><p><strong>Дано:</strong></p><p>$F = -3$ см</p><p>$(a+b) = 4$ см</p><p>$F = -0.03$ м</p><p>$(a+b) = 0.04$ м</p><p><strong>Найти:</strong></p><p>$D, a, b$</p><p><strong>Решение:</strong></p><p>Найдем оптическую силу $D$, переведя $F$ в метры: $F = -3$ см $= -0.03$ м.</p><p>$D = \frac{1}{F} = \frac{1}{-0.03} = -\frac{100}{3}$ дптр $\approx -33.33$ дптр.</p><p>Решим систему уравнений:</p><p>1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-3}$</p><p>2) $a+b = 4 \Rightarrow a = 4 - b$</p><p>Подставим (2) в (1): $\frac{1}{4-b} + \frac{1}{b} = -\frac{1}{3}$.</p><p>Приведем к общему знаменателю: $\frac{b + 4 - b}{b(4-b)} = -\frac{1}{3} \Rightarrow \frac{4}{4b-b^2} = -\frac{1}{3}$.</p><p>Отсюда $12 = -(4b-b^2)$, что приводит к квадратному уравнению $b^2 - 4b - 12 = 0$.</p><p>По теореме Виета, корни уравнения $b_1=6$ и $b_2=-2$.</p><p>Так как изображение мнимое, $b$ должно быть отрицательным. Следовательно, $b = -2$ см.</p><p>Найдем $a$: $a = 4 - b = 4 - (-2) = 6$ см.</p><p><strong>Ответ:</strong> $D = -100/3$ дптр; $a = 6$ см; $b = -2$ см.</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" => "1435329" "type" => "task" ] "previous" => array:2 [ "refs" => "1435327" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\BookPage {#1154 #connection: "mysql" #table: "book_pages" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false 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{#1360} "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 {#1361} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1362} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1363} "content" => Illuminate\Database\Eloquent\Collection {#1365} "next" => array:2 [ "refs" => "1435327" "type" => "task" ] "previous" => array:2 [ "refs" => "1435325" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1371} "page" => array:2 [ "refs" => "1435687" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1366 #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" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1364 #items: array:1 [ 0 => App\Models\Term {#1036} ] #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 {#1373 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1369 #items: array:1 [ 0 => App\Models\Branch {#1198} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1367 #items: array:3 [ 0 => App\Models\Branch {#1198} 1 => App\Models\Branch {#1202} 2 => App\Models\Branch {#1207} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1368 #items: array:2 [ 0 => App\Models\Element {#1386 …30} 1 => App\Models\Element {#1388 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435328" "type" => "task" ] "previous" => array:2 [ "refs" => "1435326" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1383 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1435687" "type" => "book_page" ] ] #original: array:24 [ "id" => 1435327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1364} "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 {#1373} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1369} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1367} "content" => Illuminate\Database\Eloquent\Collection {#1368} "next" => array:2 [ "refs" => "1435328" "type" => "task" ] "previous" => array:2 [ "refs" => "1435326" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1383} "page" => array:2 [ "refs" => "1435687" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] 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null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1385 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 #items: array:1 [ 0 => App\Models\Branch {#1198} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1379 #items: array:3 [ 0 => App\Models\Branch {#1198} 1 => App\Models\Branch {#1202} 2 => App\Models\Branch {#1207} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1382 #items: array:2 [ 0 => App\Models\Element {#1182} 1 => App\Models\Element {#1175} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1435329" "type" => "task" ] "previous" => array:2 [ "refs" => "1435327" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1380 #items: array:1 [ 0 => App\Models\Book {#1049} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1435687" "type" => "book_page" ] ] #original: array:24 [ "id" => 1435328 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1370} "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 {#1385} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1379} "content" => Illuminate\Database\Eloquent\Collection {#1382} "next" => array:2 [ "refs" => "1435329" "type" => "task" ] "previous" => array:2 [ "refs" => "1435327" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1380} "page" => array:2 [ "refs" => "1435687" "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 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1435687 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-52" "field_display_title" => "52" "field_folder" => "3" "field_image_name" => "52" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1168} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1166} "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 {#1165} "content" => Illuminate\Database\Eloquent\Collection {#1151} "next" => array:2 [ "refs" => "1435688" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435686" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1349} ] #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" => 1435328 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "52" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/49-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" 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#fillable: [] #guarded: array:1 [ 0 => "*" ] }
№6 (с. 52)
Условие. №6 (с. 52)
скриншот условия
6. Точечный источник света находится на расстоянии $\text{a}$ от главной плоскости тонкой рассеивающей линзы с фокусным расстоянием $\text{F}$ и оптической силой $\text{D}$. Заполните таблицу, определив неизвестные величины. Здесь $\text{b}$ — расстояние от главной плоскости линзы до изображения источника.
| № линзы | $\text{F}$, см | $\text{D}$, дптр | $\text{a}$, см | $\text{b}$, см | $(a+b)$, см |
|---|---|---|---|---|---|
| 1 | $-25$ | 4 | |||
| 2 | $-60$ | 30 | |||
| 3 | $-20$ | $-40/3$ | |||
| 4 | $-6$ | $-2$ | |||
| 5* | $-50$ | $-0,5$ | |||
| 6* | $-3$ | 4 |
Решение. №6 (с. 52)
Для решения задачи используются формула тонкой линзы и формула для оптической силы. Поскольку линза рассеивающая, ее фокусное расстояние $F$ и оптическая сила $D$ являются отрицательными величинами. Источник света считается действительным, поэтому расстояние до него $a$ всегда положительно. Для рассеивающей линзы изображение действительного источника всегда мнимое, поэтому расстояние до изображения $b$ будет отрицательным.
Основная формула тонкой линзы: $\frac{1}{a} + \frac{1}{b} = \frac{1}{F}$
Связь оптической силы $D$ (в диоптриях, дптр) и фокусного расстояния $F$ (в метрах, м): $D = \frac{1}{F}$
1. Линза № 1Дано:
$D = -25$ дптр
$a = 4$ см
$a = 0.04$ м
Найти:
$F, b, (a+b)$
Решение:
Найдем фокусное расстояние $F$, используя значение оптической силы $D$. Фокусное расстояние должно быть выражено в метрах.
$F = \frac{1}{D} = \frac{1}{-25} = -0.04$ м.
Переведем $F$ в сантиметры: $F = -4$ см.
Теперь воспользуемся формулой тонкой линзы для нахождения $b$. Расчеты будем вести в сантиметрах.
$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-4} - \frac{1}{4} = -\frac{2}{4} = -\frac{1}{2}$ см$^{-1}$.
Отсюда $b = -2$ см.
Вычислим сумму $(a+b)$:
$(a+b) = 4 \text{ см} + (-2 \text{ см}) = 2$ см.
Ответ: $F = -4$ см; $b = -2$ см; $(a+b) = 2$ см.
2. Линза № 2Дано:
$F = -60$ см
$a = 30$ см
$F = -0.6$ м
$a = 0.3$ м
Найти:
$D, b, (a+b)$
Решение:
Найдем оптическую силу $D$. Для этого фокусное расстояние $F$ нужно перевести в метры: $F = -60$ см $= -0.6$ м.
$D = \frac{1}{F} = \frac{1}{-0.6} = -\frac{10}{6} = -\frac{5}{3}$ дптр $\approx -1.67$ дптр.
Найдем расстояние до изображения $b$ по формуле тонкой линзы (в см):
$\frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{1}{-60} - \frac{1}{30} = -\frac{1}{60} - \frac{2}{60} = -\frac{3}{60} = -\frac{1}{20}$ см$^{-1}$.
Отсюда $b = -20$ см.
Вычислим сумму $(a+b)$:
$(a+b) = 30 \text{ см} + (-20 \text{ см}) = 10$ см.
Ответ: $D = -5/3$ дптр; $b = -20$ см; $(a+b) = 10$ см.
3. Линза № 3Дано:
$F = -20$ см
$b = -40/3$ см
$F = -0.2$ м
$b \approx -0.133$ м
Найти:
$D, a, (a+b)$
Решение:
Найдем оптическую силу $D$, переведя $F$ в метры: $F = -20$ см $= -0.2$ м.
$D = \frac{1}{F} = \frac{1}{-0.2} = -5$ дптр.
Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):
$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-20} - \frac{1}{-40/3} = -\frac{1}{20} + \frac{3}{40} = -\frac{2}{40} + \frac{3}{40} = \frac{1}{40}$ см$^{-1}$.
Отсюда $a = 40$ см.
Вычислим сумму $(a+b)$:
$(a+b) = 40 \text{ см} + (-\frac{40}{3} \text{ см}) = \frac{120-40}{3} = \frac{80}{3}$ см.
Ответ: $D = -5$ дптр; $a = 40$ см; $(a+b) = 80/3$ см.
4. Линза № 4Дано:
$F = -6$ см
$b = -2$ см
$F = -0.06$ м
$b = -0.02$ м
Найти:
$D, a, (a+b)$
Решение:
Найдем оптическую силу $D$, переведя $F$ в метры: $F = -6$ см $= -0.06$ м.
$D = \frac{1}{F} = \frac{1}{-0.06} = -\frac{100}{6} = -\frac{50}{3}$ дптр $\approx -16.67$ дптр.
Найдем расстояние до источника $a$ по формуле тонкой линзы (в см):
$\frac{1}{a} = \frac{1}{F} - \frac{1}{b} = \frac{1}{-6} - \frac{1}{-2} = -\frac{1}{6} + \frac{1}{2} = -\frac{1}{6} + \frac{3}{6} = \frac{2}{6} = \frac{1}{3}$ см$^{-1}$.
Отсюда $a = 3$ см.
Вычислим сумму $(a+b)$:
$(a+b) = 3 \text{ см} + (-2 \text{ см}) = 1$ см.
Ответ: $D = -50/3$ дптр; $a = 3$ см; $(a+b) = 1$ см.
5. Линза № 5*Дано:
$D = -50$ дптр
$(a+b) = -0.5$ см
$(a+b) = -0.005$ м
Найти:
$F, a, b$
Решение:
Найдем фокусное расстояние $F$:
$F = \frac{1}{D} = \frac{1}{-50} = -0.02$ м $= -2$ см.
Для рассеивающей линзы и действительного источника ($a > 0$) изображение всегда мнимое ($b < 0$), причем по модулю расстояние до изображения меньше расстояния до источника ($|b| < a$).
Из условия $(a+b) = -0.5$ выразим $a$: $a = -0.5 - b$.
Проверим условие $a > 0$: $-0.5 - b > 0$, что означает $b < -0.5$ см.
Проверим условие $|b| < a$. Поскольку $b < 0$, то $|b| = -b$. Подставим в неравенство:
$-b < -0.5 - b \Rightarrow 0 < -0.5$.
Полученное неравенство ложно. Это означает, что исходные данные противоречат законам оптики и задача с такими данными не имеет физического решения. Вероятно, в условии допущена опечатка.
Предположим, что в условии имелось в виду $(a+b) = 0.5$ см. Решим задачу для этого случая.
Имеем систему уравнений:
1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-2}$
2) $a+b = 0.5 \Rightarrow a = 0.5 - b$
Подставим (2) в (1): $\frac{1}{0.5-b} + \frac{1}{b} = -\frac{1}{2}$.
Приведем к общему знаменателю: $\frac{b + 0.5 - b}{b(0.5-b)} = -\frac{1}{2} \Rightarrow \frac{0.5}{0.5b - b^2} = -\frac{1}{2}$.
Отсюда $1 = -(0.5b - b^2)$, что приводит к квадратному уравнению $b^2 - 0.5b - 1 = 0$.
Дискриминант $D_q = (-0.5)^2 - 4(1)(-1) = 0.25 + 4 = 4.25$.
Корни $b = \frac{0.5 \pm \sqrt{4.25}}{2}$. Так как $b<0$, выбираем корень со знаком минус:
$b = \frac{0.5 - \sqrt{4.25}}{2} = \frac{1 - \sqrt{17}}{4}$ см.
Тогда $a = 0.5 - b = \frac{1}{2} - \frac{1 - \sqrt{17}}{4} = \frac{2 - 1 + \sqrt{17}}{4} = \frac{1 + \sqrt{17}}{4}$ см.
Ответ: Исходные данные противоречивы. При предположении, что $(a+b) = 0.5$ см, ответ: $F = -2$ см; $a = \frac{1 + \sqrt{17}}{4}$ см; $b = \frac{1 - \sqrt{17}}{4}$ см.
6. Линза № 6*Дано:
$F = -3$ см
$(a+b) = 4$ см
$F = -0.03$ м
$(a+b) = 0.04$ м
Найти:
$D, a, b$
Решение:
Найдем оптическую силу $D$, переведя $F$ в метры: $F = -3$ см $= -0.03$ м.
$D = \frac{1}{F} = \frac{1}{-0.03} = -\frac{100}{3}$ дптр $\approx -33.33$ дптр.
Решим систему уравнений:
1) $\frac{1}{a} + \frac{1}{b} = \frac{1}{-3}$
2) $a+b = 4 \Rightarrow a = 4 - b$
Подставим (2) в (1): $\frac{1}{4-b} + \frac{1}{b} = -\frac{1}{3}$.
Приведем к общему знаменателю: $\frac{b + 4 - b}{b(4-b)} = -\frac{1}{3} \Rightarrow \frac{4}{4b-b^2} = -\frac{1}{3}$.
Отсюда $12 = -(4b-b^2)$, что приводит к квадратному уравнению $b^2 - 4b - 12 = 0$.
По теореме Виета, корни уравнения $b_1=6$ и $b_2=-2$.
Так как изображение мнимое, $b$ должно быть отрицательным. Следовательно, $b = -2$ см.
Найдем $a$: $a = 4 - b = 4 - (-2) = 6$ см.
Ответ: $D = -100/3$ дптр; $a = 6$ см; $b = -2$ см.
Другие задания:
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