gdz.top
Номер 186, страница 284 - гдз по физике 8 класс учебник Громов, Родина
Авторы: Громов С. В., Родина Н. А., Белага В. В., Ломаченков И. А., Панебратцев Ю. А.
Тип: Учебник
Серия: классический курс
Издательство: Просвещение
Год издания: 2018 - 2026
Цвет обложки: синий
ISBN: 978-5-09-052825-2
Популярные ГДЗ в 8 классе
Задачи и упражнения - номер 186, страница 284.
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" => 1613053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-186" "field_display_title" => "186" "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" => 1612241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи и упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "266" "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 {#1048 #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" => 3654 "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 {#1050 #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: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 {#1051 #items: array:1 [ 0 => App\Models\Term {#1052 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #original: array:6 [ "id" => 5457 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "8" "field_cases" => array:6 [ "field_accusative_case" => "восьмой" "field_creative_case" => "восьмым" "field_dative_case" => "восьмому" "field_genitive_case" => "восьмого" "field_nominative_case" => "восьмой" "field_prepositional_case" => "восьмом" ] "field_translit" => "vosmoj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053 #items: array:1 [ 0 => App\Models\Term {#1054 #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 {#1055 #items: array:5 [ 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:12 [ "id" => 4194 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Громов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Сергей" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4194 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Громов" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Сергей" "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 {#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" => 5604 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Родина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Надежда" "field_patronymic" => "Александровна" "field_surname_rp" => null ] #original: array:12 [ "id" => 5604 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Родина" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Надежда" "field_patronymic" => "Александровна" "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 {#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" => 3824 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Белага" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Виктория" "field_patronymic" => "Владимировна" "field_surname_rp" => null ] #original: array:12 [ "id" => 3824 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Белага" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Виктория" "field_patronymic" => "Владимировна" "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 {#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" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Ломаченков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Иван" "field_patronymic" => "Алексеевич" "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 => "*" ] } 4 => 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" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #original: array:12 [ "id" => 5412 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Панебратцев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Юрий" "field_patronymic" => "Анатольевич" "field_surname_rp" => "Панебратцева" ] #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" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "учебник" "field_creative_case" => "учебником" "field_dative_case" => "учебнику" "field_genitive_case" => "учебника" "field_nominative_case" => "учебник" "field_prepositional_case" => "учебнике" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#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: 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:8 [ "id" => 4718 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "классический курс" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "klassicheskiy kurs" ] #original: array:8 [ "id" => 4718 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "классический курс" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "klassicheskiy kurs" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1070 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1071 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072 #items: array:1 [ 0 => App\Models\Term {#1073 #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" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075 #items: array:1 [ 0 => App\Models\Term {#1060} ] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2018" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "830" "field_priority" => null "field_default_folder" => "/fizika_08/gromov-u/" "field_isbn" => "978-5-09-052825-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517" "alt" => "" "width" => "1881" "height" => "2469" ] ] "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" => "/8-klass/fizika/gromov-uchebnik" "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" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 3654 "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 {#1050} "field_class" => Illuminate\Database\Eloquent\Collection {#1051} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1053} "field_author" => Illuminate\Database\Eloquent\Collection {#1055} "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 {#1070} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1071} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1072} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1074} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1075} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2018" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие для общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "830" "field_priority" => null "field_default_folder" => "/fizika_08/gromov-u/" "field_isbn" => "978-5-09-052825-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/gromov-u/covers/cover1.webp?ts=1763397517" "alt" => "" "width" => "1881" "height" => "2469" ] ] "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" => "/8-klass/fizika/gromov-uchebnik" "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" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1081 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1612241 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Задачи и упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1047} "field_page_start" => "266" "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 {#1038 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1034 #items: array:2 [ 0 => App\Models\Element {#1087 #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" => 1850779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Edition {#1088 #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" => 6892 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Term {#1089 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1091 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6892 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1090} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1091} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1092} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1093} "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" => "1613053" "type" => "task" ] "text" => "<p><strong>186.</strong> Постройте изображения, даваемые собирающей линзой в случаях, показанных на рисунке 27.</p><p>Рис. 27</p>" "img" => array:2 [ 0 => array:5 [ "name" => "186-1.jpg" "alt" => null "width" => "1705" "height" => 216 "path" => "/media/fizika_08/gromov-u/0-upr/186-1.webp?ts=1763478135" ] 1 => array:5 [ "name" => "186-2.jpg" "alt" => null "width" => "1365" "height" => 471 "path" => "/media/fizika_08/gromov-u/0-upr/186-2.webp?ts=1763478135" ] ] ] #original: array:7 [ "id" => 1850779 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1096} "task" => array:2 [ "refs" => "1613053" "type" => "task" ] "text" => "<p><strong>186.</strong> Постройте изображения, даваемые собирающей линзой в случаях, показанных на рисунке 27.</p><p>Рис. 27</p>" "img" => array:2 [ 0 => array:5 [ "name" => "186-1.jpg" "alt" => null "width" => "1705" "height" => 216 "path" => "/media/fizika_08/gromov-u/0-upr/186-1.webp?ts=1763478135" ] 1 => array:5 [ "name" => "186-2.jpg" "alt" => null "width" => "1365" "height" => 471 "path" => "/media/fizika_08/gromov-u/0-upr/186-2.webp?ts=1763478135" ] ] ] #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 {#1094 #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" => 1900840 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104 #items: array:1 [ 0 => App\Models\Edition {#1095 #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" => 7854 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098 #items: array:1 [ 0 => App\Models\Term {#1097 …30} ] #escapeWhenCastingToString: false } "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 7854 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1098} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1100} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1101} "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" => "1613053" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p><strong>Решение</strong></p><p>Для построения изображения стрелки необходимо построить изображения её конечных точек - основания (точка А) и острия (точка В).</p><p><strong>1.</strong> Построим изображение острия стрелки (точка В). Для этого из этой точки проведём два стандартных луча:</p><ul><li>Первый луч (показан красным) пускаем параллельно главной оптической оси. После преломления в линзе он пройдёт через её задний фокус $\text{F}$.</li><li>Второй луч (показан зелёным) пускаем через оптический центр линзы. Этот луч не преломляется и не меняет своего направления.</li></ul><p>Точка пересечения этих двух преломлённых лучей даст действительное изображение острия стрелки (точка В').</p><p><strong>2.</strong> Основание стрелки (точка А) лежит на главной оптической оси. Его изображение (точка А') также будет лежать на главной оптической оси. Его положение можно найти, проведя аналогичное построение для этой точки (например, с помощью вспомогательного луча) или воспользовавшись формулой тонкой линзы. Изображение основания окажется между фокусом $\text{F}$ и двойным фокусом $\text{2F}$ с другой стороны линзы.</p><p><strong>3.</strong> Соединив изображение основания А' с изображением острия В', получим изображение всей стрелки.</p><p>Итоговое изображение обладает следующими характеристиками:</p><ul><li><strong>Действительное</strong>, так как образовано пересечением самих преломлённых лучей.</li><li><strong>Перевёрнутое</strong>.</li><li><strong>Уменьшенное</strong>.</li><li>Расположено между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$).</li></ul><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе для случая а" style="width:100%;"><p><strong>Ответ:</strong> Изображение действительное, перевёрнутое, уменьшенное, находится за линзой на расстоянии между фокусным ($\text{F}$) и двойным фокусным ($\text{2F}$).</p><p><strong>б)</strong></p><p><strong>Решение</strong></p><p>Предмет находится между фокусом и оптическим центром линзы. Построение выполняется аналогично предыдущему случаю для точек основания (А) и острия (В).</p><p><strong>1.</strong> Построим изображение острия стрелки (точка В). Проведём два луча:</p><ul><li>Первый луч (показан красным), параллельный главной оптической оси, который после преломления пройдёт через задний фокус $\text{F}$.</li><li>Второй луч (показан зелёным), проходящий через оптический центр линзы без преломления.</li></ul><p>За линзой эти два луча расходятся. Чтобы найти изображение, необходимо мысленно продлить их в обратную сторону (влево от линзы). Точка, где пересекутся их продолжения, и будет мнимым изображением острия стрелки (точка В').</p><p><strong>2.</strong> Изображение основания стрелки (точка А), лежащего на главной оптической оси, также будет мнимым и будет лежать на главной оптической оси с той же стороны, что и предмет (точка А').</p><p><strong>3.</strong> Соединив изображения конечных точек А' и В', получим полное мнимое изображение стрелки.</p><p>Итоговое изображение обладает следующими характеристиками:</p><ul><li><strong>Мнимое</strong>, так как образовано пересечением продолжений преломлённых лучей.</li><li><strong>Прямое</strong> (неперевёрнутое).</li><li><strong>Увеличенное</strong>.</li><li>Расположено с той же стороны от линзы, что и сам предмет.</li></ul><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе для случая б" style="width:100%;"><p><strong>Ответ:</strong> Изображение мнимое, прямое, увеличенное, находится с той же стороны от линзы, что и предмет.</p>" ] #original: array:6 [ "id" => 1900840 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1104} "task" => array:2 [ "refs" => "1613053" "type" => "task" ] "text" => "<p><strong>а)</strong></p><p><strong>Решение</strong></p><p>Для построения изображения стрелки необходимо построить изображения её конечных точек - основания (точка А) и острия (точка В).</p><p><strong>1.</strong> Построим изображение острия стрелки (точка В). Для этого из этой точки проведём два стандартных луча:</p><ul><li>Первый луч (показан красным) пускаем параллельно главной оптической оси. После преломления в линзе он пройдёт через её задний фокус $\text{F}$.</li><li>Второй луч (показан зелёным) пускаем через оптический центр линзы. Этот луч не преломляется и не меняет своего направления.</li></ul><p>Точка пересечения этих двух преломлённых лучей даст действительное изображение острия стрелки (точка В').</p><p><strong>2.</strong> Основание стрелки (точка А) лежит на главной оптической оси. Его изображение (точка А') также будет лежать на главной оптической оси. Его положение можно найти, проведя аналогичное построение для этой точки (например, с помощью вспомогательного луча) или воспользовавшись формулой тонкой линзы. Изображение основания окажется между фокусом $\text{F}$ и двойным фокусом $\text{2F}$ с другой стороны линзы.</p><p><strong>3.</strong> Соединив изображение основания А' с изображением острия В', получим изображение всей стрелки.</p><p>Итоговое изображение обладает следующими характеристиками:</p><ul><li><strong>Действительное</strong>, так как образовано пересечением самих преломлённых лучей.</li><li><strong>Перевёрнутое</strong>.</li><li><strong>Уменьшенное</strong>.</li><li>Расположено между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$).</li></ul><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе для случая а" style="width:100%;"><p><strong>Ответ:</strong> Изображение действительное, перевёрнутое, уменьшенное, находится за линзой на расстоянии между фокусным ($\text{F}$) и двойным фокусным ($\text{2F}$).</p><p><strong>б)</strong></p><p><strong>Решение</strong></p><p>Предмет находится между фокусом и оптическим центром линзы. Построение выполняется аналогично предыдущему случаю для точек основания (А) и острия (В).</p><p><strong>1.</strong> Построим изображение острия стрелки (точка В). Проведём два луча:</p><ul><li>Первый луч (показан красным), параллельный главной оптической оси, который после преломления пройдёт через задний фокус $\text{F}$.</li><li>Второй луч (показан зелёным), проходящий через оптический центр линзы без преломления.</li></ul><p>За линзой эти два луча расходятся. Чтобы найти изображение, необходимо мысленно продлить их в обратную сторону (влево от линзы). Точка, где пересекутся их продолжения, и будет мнимым изображением острия стрелки (точка В').</p><p><strong>2.</strong> Изображение основания стрелки (точка А), лежащего на главной оптической оси, также будет мнимым и будет лежать на главной оптической оси с той же стороны, что и предмет (точка А').</p><p><strong>3.</strong> Соединив изображения конечных точек А' и В', получим полное мнимое изображение стрелки.</p><p>Итоговое изображение обладает следующими характеристиками:</p><ul><li><strong>Мнимое</strong>, так как образовано пересечением продолжений преломлённых лучей.</li><li><strong>Прямое</strong> (неперевёрнутое).</li><li><strong>Увеличенное</strong>.</li><li>Расположено с той же стороны от линзы, что и сам предмет.</li></ul><img src="data:image/svg+xml;base64,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" alt="Построение изображения в собирающей линзе для случая б" style="width:100%;"><p><strong>Ответ:</strong> Изображение мнимое, прямое, увеличенное, находится с той же стороны от линзы, что и предмет.</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" => "1613054" "type" => "task" ] "previous" => array:2 [ "refs" => "1613052" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ 0 => App\Models\BookPage {#1082 #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" => 1613357 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_url" => "/8-klass/fizika/gromov-uchebnik/page-284" "field_display_title" => "284" "field_folder" => "1" "field_image_name" => "284" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1102 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1048} ] #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 {#1105 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Element {#1114 #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" => 1851068 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116 #items: array:1 [ 0 => App\Models\Edition {#1088} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "284-1.jpg" "alt" => null "width" => "1875" "height" => 2557 "path" => "/media/fizika_08/gromov-u/0-1/284-1.webp?ts=1763478470" ] ] ] #original: array:6 [ "id" => 1851068 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1116} "book_page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "284-1.jpg" "alt" => null "width" => "1875" "height" => 2557 "path" => "/media/fizika_08/gromov-u/0-1/284-1.webp?ts=1763478470" ] ] ] #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" => "1613358" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1613356" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:8 [ 0 => App\Models\Task {#1187 #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" => 1613047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-180" "field_display_title" => "180" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1188 #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 {#1189 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1190 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1191 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1193 #items: array:2 [ 0 => App\Models\Element {#1202 …30} 1 => App\Models\Element {#1204 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613048" "type" => "task" ] "previous" => array:2 [ "refs" => "1613046" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1199 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613047 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-180" "field_display_title" => "180" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1188} "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 {#1189} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1190} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1191} "content" => Illuminate\Database\Eloquent\Collection {#1193} "next" => array:2 [ "refs" => "1613048" "type" => "task" ] "previous" => array:2 [ "refs" => "1613046" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1199} "page" => array:2 [ "refs" => "1613357" "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 {#1194 #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" => 1613048 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-181" "field_display_title" => "181" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1192 #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 {#1201 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1197 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1195 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1196 #items: array:2 [ 0 => App\Models\Element {#1214 …30} 1 => App\Models\Element {#1216 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613049" "type" => "task" ] "previous" => array:2 [ "refs" => "1613047" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1211 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613048 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-181" "field_display_title" => "181" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1192} "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 {#1201} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1197} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1195} "content" => Illuminate\Database\Eloquent\Collection {#1196} "next" => array:2 [ "refs" => "1613049" "type" => "task" ] "previous" => array:2 [ "refs" => "1613047" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1211} "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1206 #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" => 1613049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-182" "field_display_title" => "182" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198 #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 {#1213 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1209 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1207 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1208 #items: array:2 [ 0 => App\Models\Element {#1226 …30} 1 => App\Models\Element {#1228 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613050" "type" => "task" ] "previous" => array:2 [ "refs" => "1613048" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613049 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-182" "field_display_title" => "182" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1198} "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 {#1213} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1209} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1207} "content" => Illuminate\Database\Eloquent\Collection {#1208} "next" => array:2 [ "refs" => "1613050" "type" => "task" ] "previous" => array:2 [ "refs" => "1613048" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1223} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] } 3 => App\Models\Task {#1218 #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" => 1613050 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-183" "field_display_title" => "183" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210 #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 {#1225 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1220 #items: array:2 [ 0 => App\Models\Element {#1238 …30} 1 => App\Models\Element {#1240 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613051" "type" => "task" ] "previous" => array:2 [ "refs" => "1613049" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235 #items: array:1 [ 0 => App\Models\Book {#1048} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613050 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-183" "field_display_title" => "183" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1210} "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 {#1225} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1221} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1219} "content" => Illuminate\Database\Eloquent\Collection {#1220} "next" => array:2 [ "refs" => "1613051" "type" => "task" ] "previous" => array:2 [ "refs" => "1613049" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1235} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] } 4 => App\Models\Task {#1230 #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" => 1613051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-184" "field_display_title" => "184" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1222 #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 {#1237 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1233 #items: array:1 [ 0 => App\Models\Branch {#1045} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1232 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613052" "type" => "task" ] "previous" => array:2 [ "refs" => "1613050" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1247 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613051 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-184" "field_display_title" => "184" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1222} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1237} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1233} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1231} "content" => Illuminate\Database\Eloquent\Collection {#1232} "next" => array:2 [ "refs" => "1613052" "type" => "task" ] "previous" => array:2 [ "refs" => "1613050" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1247} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] } 5 => App\Models\Task {#1242 #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" => 1613052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-185" "field_display_title" => "185" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1234 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1249 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1245 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1244 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613053" "type" => "task" ] "previous" => array:2 [ "refs" => "1613051" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1259 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613052 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-185" "field_display_title" => "185" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1234} "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 {#1249} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1245} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1243} "content" => Illuminate\Database\Eloquent\Collection {#1244} "next" => array:2 [ "refs" => "1613053" "type" => "task" ] "previous" => array:2 [ "refs" => "1613051" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1259} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] } 6 => App\Models\Task {#1254 #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" => 1613053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-186" "field_display_title" => "186" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1261 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1257 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1255 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1258 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613054" "type" => "task" ] "previous" => array:2 [ "refs" => "1613052" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1256 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-186" "field_display_title" => "186" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1246} "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 {#1261} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1257} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1255} "content" => Illuminate\Database\Eloquent\Collection {#1258} "next" => array:2 [ "refs" => "1613054" "type" => "task" ] "previous" => array:2 [ "refs" => "1613052" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1256} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] } 7 => App\Models\Task {#1266 #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" => 1613054 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-187" "field_display_title" => "187" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1268 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:1 [ …1] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270 #items: array:1 [ …1] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1272 #items: array:2 [ …2] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1613055" "type" => "task" ] "previous" => array:2 [ "refs" => "1613053" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1278 #items: array:1 [ …1] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1613357" "type" => "book_page" ] ] #original: array:24 [ "id" => 1613054 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-187" "field_display_title" => "187" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1267} "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 {#1268} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1269} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1270} "content" => Illuminate\Database\Eloquent\Collection {#1272} "next" => array:2 [ "refs" => "1613055" "type" => "task" ] "previous" => array:2 [ "refs" => "1613053" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1278} "page" => array:2 [ "refs" => "1613357" "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" => 1613357 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_url" => "/8-klass/fizika/gromov-uchebnik/page-284" "field_display_title" => "284" "field_folder" => "1" "field_image_name" => "284" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1102} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1103} "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 {#1105} "content" => Illuminate\Database\Eloquent\Collection {#1115} "next" => array:2 [ "refs" => "1613358" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1613356" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1173} ] #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" => 1613053 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "284" "field_page_end" => null "field_url" => "/8-klass/fizika/gromov-uchebnik/upr-186" "field_display_title" => "186" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1037} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1035} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1046} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1038} "content" => Illuminate\Database\Eloquent\Collection {#1034} "next" => array:2 [ "refs" => "1613054" "type" => "task" ] "previous" => array:2 [ "refs" => "1613052" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1084} "page" => array:2 [ "refs" => "1613357" "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 => "*" ] }
№186 (с. 284)
Условие. №186 (с. 284)
скриншот условия
186. Постройте изображения, даваемые собирающей линзой в случаях, показанных на рисунке 27.
Рис. 27
Решение. №186 (с. 284)
а)
Решение
Для построения изображения стрелки необходимо построить изображения её конечных точек - основания (точка А) и острия (точка В).
1. Построим изображение острия стрелки (точка В). Для этого из этой точки проведём два стандартных луча:
- Первый луч (показан красным) пускаем параллельно главной оптической оси. После преломления в линзе он пройдёт через её задний фокус $\text{F}$.
- Второй луч (показан зелёным) пускаем через оптический центр линзы. Этот луч не преломляется и не меняет своего направления.
Точка пересечения этих двух преломлённых лучей даст действительное изображение острия стрелки (точка В').
2. Основание стрелки (точка А) лежит на главной оптической оси. Его изображение (точка А') также будет лежать на главной оптической оси. Его положение можно найти, проведя аналогичное построение для этой точки (например, с помощью вспомогательного луча) или воспользовавшись формулой тонкой линзы. Изображение основания окажется между фокусом $\text{F}$ и двойным фокусом $\text{2F}$ с другой стороны линзы.
3. Соединив изображение основания А' с изображением острия В', получим изображение всей стрелки.
Итоговое изображение обладает следующими характеристиками:
- Действительное, так как образовано пересечением самих преломлённых лучей.
- Перевёрнутое.
- Уменьшенное.
- Расположено между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$).
Ответ: Изображение действительное, перевёрнутое, уменьшенное, находится за линзой на расстоянии между фокусным ($\text{F}$) и двойным фокусным ($\text{2F}$).
б)
Решение
Предмет находится между фокусом и оптическим центром линзы. Построение выполняется аналогично предыдущему случаю для точек основания (А) и острия (В).
1. Построим изображение острия стрелки (точка В). Проведём два луча:
- Первый луч (показан красным), параллельный главной оптической оси, который после преломления пройдёт через задний фокус $\text{F}$.
- Второй луч (показан зелёным), проходящий через оптический центр линзы без преломления.
За линзой эти два луча расходятся. Чтобы найти изображение, необходимо мысленно продлить их в обратную сторону (влево от линзы). Точка, где пересекутся их продолжения, и будет мнимым изображением острия стрелки (точка В').
2. Изображение основания стрелки (точка А), лежащего на главной оптической оси, также будет мнимым и будет лежать на главной оптической оси с той же стороны, что и предмет (точка А').
3. Соединив изображения конечных точек А' и В', получим полное мнимое изображение стрелки.
Итоговое изображение обладает следующими характеристиками:
- Мнимое, так как образовано пересечением продолжений преломлённых лучей.
- Прямое (неперевёрнутое).
- Увеличенное.
- Расположено с той же стороны от линзы, что и сам предмет.
Ответ: Изображение мнимое, прямое, увеличенное, находится с той же стороны от линзы, что и предмет.
Другие задания:
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Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №186 (с. 284), авторов: Громов (Сергей Васильевич), Родина (Надежда Александровна), Белага (Виктория Владимировна), Ломаченков (Иван Алексеевич), Панебратцев (Юрий Анатольевич), ФГОС (старый) учебного пособия издательства Просвещение.