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Вариант 2, страница 85 - гдз по физике 9 класс дидактические материалы Марон, Марон
Авторы: Марон А. Е., Марон Е. А.
Тип: Дидактические материалы
Издательство: Просвещение
Год издания: 2022 - 2026
Уровень обучения: базовый
Цвет обложки: белый изображена башня
ISBN: 978-5-09-111414-0
Популярные ГДЗ в 9 классе
Самостоятельные работы. СР-15. Преломление света. Линзы - страница 85.
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" => 1428697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp15-2" "field_display_title" => "Вариант 2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1036 #items: [] #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 {#1034 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1073 #items: array:1 [ 0 => App\Models\Branch {#1035 #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" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1037 #items: array:1 [ 0 => App\Models\Book {#1039 #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" => 894 "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 {#1040 #items: array:1 [ 0 => App\Models\Term {#1041 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1042 #items: array:1 [ 0 => App\Models\Term {#1043 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1044 #items: array:1 [ 0 => App\Models\Term {#1045 #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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1046 #items: array:2 [ 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:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 1 => 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:12 [ …12] #original: array:12 [ …12] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050 #items: array:1 [ 0 => App\Models\Term {#1051 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ …10] #original: array:10 [ …10] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_country" => 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 [ …6] #original: array:6 [ …6] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } "field_city" => 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 …22 } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058 #items: array:1 [ 0 => App\Models\Term {#1059 …30} ] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060 #items: array:1 [ 0 => App\Models\Term {#1061 …30} ] #escapeWhenCastingToString: false } "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062 #items: array:1 [ 0 => App\Models\Term {#1063 …30} ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068 #items: array:1 [ 0 => App\Models\Term {#1069 …30} ] #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" => 894 "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 {#1040} "field_class" => Illuminate\Database\Eloquent\Collection {#1042} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1044} "field_author" => Illuminate\Database\Eloquent\Collection {#1046} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1049} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1050} "field_country" => Illuminate\Database\Eloquent\Collection {#1052} "field_city" => Illuminate\Database\Eloquent\Collection {#1054} "field_series" => Illuminate\Database\Eloquent\Collection {#1056} "field_umk" => Illuminate\Database\Eloquent\Collection {#1057} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1058} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1060} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1062} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1064} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1065} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1066} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1067} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1068} "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 {#1070 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1038} "field_page_start" => "53" "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 {#1037} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1070} ] #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 {#1109 #items: array:2 [ 0 => App\Models\Branch {#1117 #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" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "53" "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 {#1152 #items: array:1 [ 0 => App\Models\Book {#1119 #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" => 894 "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 {#1121 #items: array:1 [ 0 => App\Models\Term {#1120 #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 {#1122 #items: array:1 [ 0 => App\Models\Term {#1123 #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 {#1124 #items: array:1 [ 0 => App\Models\Term {#1125 #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 {#1126 #items: array:2 [ 0 => App\Models\Term {#1127 #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" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 5107 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Абрам" "field_patronymic" => "Евсеевич" "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 {#1128 #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" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5108 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Марон" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Евгений" "field_patronymic" => "Абрамович" "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 {#1129 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130 #items: array:1 [ 0 => App\Models\Term {#1131 #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" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #original: array:10 [ "id" => 6510 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Дидактические материалы" "field_book_type_foreign" => null "field_cases" => array:6 [ "field_accusative_case" => "дидактические материалы" "field_creative_case" => "дидактическими материалами" "field_dative_case" => "дидактическим материалам" "field_genitive_case" => "дидактических материалов" "field_nominative_case" => "дидактические материалы" "field_prepositional_case" => "дидактических материалах" ] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "didakticheskie materialy" ] #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 {#1132 #items: array:1 [ 0 => App\Models\Term {#1133 #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 {#1134 #items: array:1 [ 0 => App\Models\Term {#1135 #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 {#1136 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1137 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138 #items: array:1 [ 0 => App\Models\Term {#1139 #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" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #original: array:6 [ "id" => 38 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "базовый" "field_cases" => array:6 [ "field_accusative_case" => "базовый" "field_creative_case" => "базовым" "field_dative_case" => "базовому" "field_genitive_case" => "базового" "field_nominative_case" => "базовый" "field_prepositional_case" => "базовом" ] "field_translit" => "bazovyy" ] #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_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140 #items: array:1 [ 0 => App\Models\Term {#1141 #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" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "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" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #original: array:10 [ "id" => 25 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (новый)" "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" => "красный" "field_end_year" => "2027" "field_start_year" => "2023" "field_translit" => "fgos" "field_type" => "новый" ] #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" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142 #items: array:1 [ 0 => App\Models\Term {#1143 #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" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" => "pererabotannoe" ] #original: array:6 [ "id" => 34 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "переработанное" "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" => "pererabotannoe" ] #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 {#1144 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148 #items: array:1 [ 0 => App\Models\Term {#1149 #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" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #original: array:6 [ "id" => 45 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "белый" "field_cases" => array:6 [ "field_accusative_case" => "белый" "field_creative_case" => "белым" "field_dative_case" => "белому" "field_genitive_case" => "белого" "field_nominative_case" => "белый" "field_prepositional_case" => "белом" ] "field_translit" => "belyy" ] #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" => 894 "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 {#1121} "field_class" => Illuminate\Database\Eloquent\Collection {#1122} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1124} "field_author" => Illuminate\Database\Eloquent\Collection {#1126} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1129} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1130} "field_country" => Illuminate\Database\Eloquent\Collection {#1132} "field_city" => Illuminate\Database\Eloquent\Collection {#1134} "field_series" => Illuminate\Database\Eloquent\Collection {#1136} "field_umk" => Illuminate\Database\Eloquent\Collection {#1137} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1138} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1140} "field_publication_number" => "3" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1142} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1144} "field_under_the_edition_degree" => null "field_cover_description" => "изображена башня" "field_publication_year" => "2022" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебное пособие" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "674" "field_priority" => null "field_default_folder" => "/fizika_09/maron-dm/" "field_isbn" => "978-5-09-111414-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/maron-dm/covers/cover1.webp?ts=1758533880" "alt" => "" "width" => "1888" "height" => "2427" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1145} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1146} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1147} "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1148} "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 {#1150 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Самостоятельные работы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1118} "field_page_start" => "53" "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 {#1152} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1150} ] #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 {#1151 #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" => 1428189 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-15. Преломление света. Линзы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "85" "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 {#1154 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Branch {#1035} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1428189 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "СР-15. Преломление света. Линзы" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_page_start" => "85" "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 {#1154} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1155} ] #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 {#1071 #items: array:2 [ 0 => App\Models\Element {#1100 #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" => 1683012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090 #items: array:1 [ 0 => App\Models\Edition {#1098 #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" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096 #items: array:1 [ 0 => App\Models\Term {#1099 …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 {#1097 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 5992 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1096} "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 {#1097} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1094} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1095} "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" => "1428697" "type" => "task" ] "text" => "<p><strong>1.</strong> В каких случаях угол падения луча света на границу двух сред равен углу преломления?</p><p><strong>2.</strong> Постройте изображение предмета <em>AB</em> в линзе (рис. 114). Охарактеризуйте изображение.</p><p><strong>3.</strong> Оптическая сила линзы $D = 4 \text{ дптр}$. Чему равно фокусное расстояние этой линзы? Какая это линза?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1463" "height" => 473 "path" => "/media/fizika_09/maron-dm/0-cp15/2-1.webp?ts=1758964257" ] ] ] #original: array:7 [ "id" => 1683012 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1090} "task" => array:2 [ "refs" => "1428697" "type" => "task" ] "text" => "<p><strong>1.</strong> В каких случаях угол падения луча света на границу двух сред равен углу преломления?</p><p><strong>2.</strong> Постройте изображение предмета <em>AB</em> в линзе (рис. 114). Охарактеризуйте изображение.</p><p><strong>3.</strong> Оптическая сила линзы $D = 4 \text{ дптр}$. Чему равно фокусное расстояние этой линзы? Какая это линза?</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "1463" "height" => 473 "path" => "/media/fizika_09/maron-dm/0-cp15/2-1.webp?ts=1758964257" ] ] ] #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 {#1093 #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" => 1730714 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084 #items: array:1 [ 0 => App\Models\Edition {#1092 #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" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088 #items: array:1 [ 0 => App\Models\Term {#1091 …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 {#1089 #items: [] #escapeWhenCastingToString: false } "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086 #items: [] #escapeWhenCastingToString: false } "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087 #items: [] #escapeWhenCastingToString: false } "field_content_source" => null ] #original: array:21 [ "id" => 6313 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1088} "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 {#1089} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1086} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1087} "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" => "1428697" "type" => "task" ] "text" => "<p><strong>1.</strong> В каких случаях угол падения луча света на границу двух сред равен углу преломления?</p><p>Угол падения луча света на границу двух сред равен углу преломления в двух случаях. Это следует из закона преломления света (закона Снеллиуса): $n_1 \sin \alpha = n_2 \sin \gamma$, где $n_1$ и $n_2$ — показатели преломления первой и второй сред, $\alpha$ — угол падения, а $\gamma$ — угол преломления.</p><p>Равенство $\alpha = \gamma$ возможно, если:</p><p><strong>1.</strong> Луч света падает на границу раздела сред перпендикулярно. В этом случае угол падения $\alpha = 0^\circ$. Тогда из закона преломления следует, что и угол преломления $\gamma$ также будет равен $0^\circ$. Луч не меняет своего направления.</p><p><strong>2.</strong> Показатели преломления двух сред одинаковы, то есть $n_1 = n_2$. В этом случае свет проходит через границу раздела так, как будто это однородная среда, и преломления не происходит. Для любого угла падения $\alpha$ угол преломления $\gamma$ будет ему равен.</p><p><strong>Ответ:</strong> Угол падения равен углу преломления, если луч падает перпендикулярно на границу раздела двух сред или если показатели преломления этих сред одинаковы.</p><p><strong>2.</strong> Постройте изображение предмета АВ в линзе (рис. 114). Охарактеризуйте изображение.</p><p>Так как рисунок 114 не предоставлен, построим изображение предмета АВ для общего случая, когда предмет находится между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$) собирающей линзы.</p><p>Для построения изображения точки B (вершины предмета) используем два луча с известным ходом:</p><p>• Луч, идущий от точки B параллельно главной оптической оси. После преломления в линзе он пройдет через ее задний фокус $F'$.</p><p>• Луч, идущий от точки B через оптический центр линзы O. Этот луч не преломляется и не меняет своего направления.</p><p>Точка B', где пересекутся эти два луча после прохождения через линзу, будет действительным изображением точки B. Опустив перпендикуляр из точки B' на главную оптическую ось, получим точку A' — изображение точки A. Таким образом, A'B' — это искомое изображение предмета АВ.</p><svg width="650" height="300" xmlns="http://www.w3.org/2000/svg" style="display: block; margin: 1em auto;"><!-- Главная оптическая ось --><line x1="0" y1="150" x2="650" y2="150" stroke="black" stroke-width="1" stroke-dasharray="5 5"></line><!-- Линза --><line x1="300" y1="20" x2="300" y2="280" stroke="black" stroke-width="2"></line><path d="M 300 20 L 290 30 M 300 20 L 310 30" stroke="black" fill="none" stroke-width="2"></path><path d="M 300 280 L 290 270 M 300 280 L 310 270" stroke="black" fill="none" stroke-width="2"></path><text x="305" y="20" font-family="Arial" font-size="16">L</text><!-- Фокусы и двойные фокусы --><circle cx="200" cy="150" r="3" fill="black"></circle><text x="195" y="140" font-family="Arial" font-size="16">F</text><circle cx="100" cy="150" r="3" fill="black"></circle><text x="90" y="140" font-family="Arial" font-size="16">2F</text><circle cx="400" cy="150" r="3" fill="black"></circle><text x="395" y="140" font-family="Arial" font-size="16">F'</text><circle cx="500" cy="150" r="3" fill="black"></circle><text x="490" y="140" font-family="Arial" font-size="16">2F'</text><circle cx="300" cy="150" r="3" fill="black"></circle><text x="305" y="165" font-family="Arial" font-size="16">O</text><!-- Предмет AB --><line x1="150" y1="150" x2="150" y2="100" stroke="blue" stroke-width="3"></line><path d="M 150 100 L 145 110 M 150 100 L 155 110" stroke="blue" fill="none" stroke-width="3"></path><text x="140" y="170" font-family="Arial" font-size="16" fill="blue">A</text><text x="140" y="95" font-family="Arial" font-size="16" fill="blue">B</text><!-- Луч 1 (параллельный) --><line x1="150" y1="100" x2="300" y2="100" stroke="red" stroke-width="1.5"></line><line x1="300" y1="100" x2="600" y2="250" stroke="red" stroke-width="1.5" stroke-dasharray="4 4"></line><!-- Луч 2 (через центр) --><line x1="150" y1="100" x2="600" y2="250" stroke="green" stroke-width="1.5" stroke-dasharray="4 4"></line><!-- Изображение A'B' --><line x1="600" y1="150" x2="600" y2="250" stroke="purple" stroke-width="3"></line><path d="M 600 250 L 595 240 M 600 250 L 605 240" stroke="purple" fill="none" stroke-width="3"></path><text x="590" y="145" font-family="Arial" font-size="16" fill="purple">A'</text><text x="590" y="270" font-family="Arial" font-size="16" fill="purple">B'</text></svg><p>Характеристика полученного изображения A'B':</p><p>• <strong>Действительное</strong>, так как получено на пересечении самих преломленных лучей, а не их продолжений.</p><p>• <strong>Перевернутое</strong>, так как изображение направлено в противоположную сторону относительно главной оптической оси по сравнению с предметом.</p><p>• <strong>Увеличенное</strong>, так как его линейные размеры больше размеров предмета.</p><p><strong>Ответ:</strong> Изображение, полученное в собирающей линзе для предмета, расположенного между фокусом и двойным фокусом, является действительным, перевернутым и увеличенным.</p><p><strong>3.</strong> Оптическая сила линзы D = 4 дптр. Чему равно фокусное расстояние этой линзы? Какая это линза?</p><p><strong>Дано:</strong></p><p>Оптическая сила линзы $D = 4$ дптр.</p><p>Единица измерения оптической силы диоптрия (дптр) связана с основной единицей длины в СИ (метр) соотношением $1 \text{ дптр} = 1 \text{ м}^{-1}$. Следовательно, $D = 4 \text{ м}^{-1}$.</p><p><strong>Найти:</strong></p><p>Фокусное расстояние $\text{F}$ — ?</p><p>Тип линзы — ?</p><p><strong>Решение:</strong></p><p>Оптическая сила линзы $\text{D}$ и ее фокусное расстояние $\text{F}$ связаны соотношением:</p><p>$D = \frac{1}{F}$</p><p>Выразим фокусное расстояние из этой формулы:</p><p>$F = \frac{1}{D}$</p><p>Подставим числовое значение оптической силы в единицах СИ:</p><p>$F = \frac{1}{4 \text{ м}^{-1}} = 0.25 \text{ м}$</p><p>Для наглядности можно перевести фокусное расстояние в сантиметры:</p><p>$F = 0.25 \text{ м} \cdot 100 \frac{\text{см}}{\text{м}} = 25 \text{ см}$</p><p>Тип линзы определяется знаком ее оптической силы. Поскольку оптическая сила $D = 4$ дптр — положительная величина ($D > 0$), то линза является <strong>собирающей</strong>.</p><p><strong>Ответ:</strong> Фокусное расстояние линзы равно $0.25$ м (или $\text{25}$ см). Линза является собирающей.</p>" ] #original: array:6 [ "id" => 1730714 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1084} "task" => array:2 [ "refs" => "1428697" "type" => "task" ] "text" => "<p><strong>1.</strong> В каких случаях угол падения луча света на границу двух сред равен углу преломления?</p><p>Угол падения луча света на границу двух сред равен углу преломления в двух случаях. Это следует из закона преломления света (закона Снеллиуса): $n_1 \sin \alpha = n_2 \sin \gamma$, где $n_1$ и $n_2$ — показатели преломления первой и второй сред, $\alpha$ — угол падения, а $\gamma$ — угол преломления.</p><p>Равенство $\alpha = \gamma$ возможно, если:</p><p><strong>1.</strong> Луч света падает на границу раздела сред перпендикулярно. В этом случае угол падения $\alpha = 0^\circ$. Тогда из закона преломления следует, что и угол преломления $\gamma$ также будет равен $0^\circ$. Луч не меняет своего направления.</p><p><strong>2.</strong> Показатели преломления двух сред одинаковы, то есть $n_1 = n_2$. В этом случае свет проходит через границу раздела так, как будто это однородная среда, и преломления не происходит. Для любого угла падения $\alpha$ угол преломления $\gamma$ будет ему равен.</p><p><strong>Ответ:</strong> Угол падения равен углу преломления, если луч падает перпендикулярно на границу раздела двух сред или если показатели преломления этих сред одинаковы.</p><p><strong>2.</strong> Постройте изображение предмета АВ в линзе (рис. 114). Охарактеризуйте изображение.</p><p>Так как рисунок 114 не предоставлен, построим изображение предмета АВ для общего случая, когда предмет находится между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$) собирающей линзы.</p><p>Для построения изображения точки B (вершины предмета) используем два луча с известным ходом:</p><p>• Луч, идущий от точки B параллельно главной оптической оси. После преломления в линзе он пройдет через ее задний фокус $F'$.</p><p>• Луч, идущий от точки B через оптический центр линзы O. Этот луч не преломляется и не меняет своего направления.</p><p>Точка B', где пересекутся эти два луча после прохождения через линзу, будет действительным изображением точки B. Опустив перпендикуляр из точки B' на главную оптическую ось, получим точку A' — изображение точки A. Таким образом, A'B' — это искомое изображение предмета АВ.</p><svg width="650" height="300" xmlns="http://www.w3.org/2000/svg" style="display: block; margin: 1em auto;"><!-- Главная оптическая ось --><line x1="0" y1="150" x2="650" y2="150" stroke="black" stroke-width="1" stroke-dasharray="5 5"></line><!-- Линза --><line x1="300" y1="20" x2="300" y2="280" stroke="black" stroke-width="2"></line><path d="M 300 20 L 290 30 M 300 20 L 310 30" stroke="black" fill="none" stroke-width="2"></path><path d="M 300 280 L 290 270 M 300 280 L 310 270" stroke="black" fill="none" stroke-width="2"></path><text x="305" y="20" font-family="Arial" font-size="16">L</text><!-- Фокусы и двойные фокусы --><circle cx="200" cy="150" r="3" fill="black"></circle><text x="195" y="140" font-family="Arial" font-size="16">F</text><circle cx="100" cy="150" r="3" fill="black"></circle><text x="90" y="140" font-family="Arial" font-size="16">2F</text><circle cx="400" cy="150" r="3" fill="black"></circle><text x="395" y="140" font-family="Arial" font-size="16">F'</text><circle cx="500" cy="150" r="3" fill="black"></circle><text x="490" y="140" font-family="Arial" font-size="16">2F'</text><circle cx="300" cy="150" r="3" fill="black"></circle><text x="305" y="165" font-family="Arial" font-size="16">O</text><!-- Предмет AB --><line x1="150" y1="150" x2="150" y2="100" stroke="blue" stroke-width="3"></line><path d="M 150 100 L 145 110 M 150 100 L 155 110" stroke="blue" fill="none" stroke-width="3"></path><text x="140" y="170" font-family="Arial" font-size="16" fill="blue">A</text><text x="140" y="95" font-family="Arial" font-size="16" fill="blue">B</text><!-- Луч 1 (параллельный) --><line x1="150" y1="100" x2="300" y2="100" stroke="red" stroke-width="1.5"></line><line x1="300" y1="100" x2="600" y2="250" stroke="red" stroke-width="1.5" stroke-dasharray="4 4"></line><!-- Луч 2 (через центр) --><line x1="150" y1="100" x2="600" y2="250" stroke="green" stroke-width="1.5" stroke-dasharray="4 4"></line><!-- Изображение A'B' --><line x1="600" y1="150" x2="600" y2="250" stroke="purple" stroke-width="3"></line><path d="M 600 250 L 595 240 M 600 250 L 605 240" stroke="purple" fill="none" stroke-width="3"></path><text x="590" y="145" font-family="Arial" font-size="16" fill="purple">A'</text><text x="590" y="270" font-family="Arial" font-size="16" fill="purple">B'</text></svg><p>Характеристика полученного изображения A'B':</p><p>• <strong>Действительное</strong>, так как получено на пересечении самих преломленных лучей, а не их продолжений.</p><p>• <strong>Перевернутое</strong>, так как изображение направлено в противоположную сторону относительно главной оптической оси по сравнению с предметом.</p><p>• <strong>Увеличенное</strong>, так как его линейные размеры больше размеров предмета.</p><p><strong>Ответ:</strong> Изображение, полученное в собирающей линзе для предмета, расположенного между фокусом и двойным фокусом, является действительным, перевернутым и увеличенным.</p><p><strong>3.</strong> Оптическая сила линзы D = 4 дптр. Чему равно фокусное расстояние этой линзы? Какая это линза?</p><p><strong>Дано:</strong></p><p>Оптическая сила линзы $D = 4$ дптр.</p><p>Единица измерения оптической силы диоптрия (дптр) связана с основной единицей длины в СИ (метр) соотношением $1 \text{ дптр} = 1 \text{ м}^{-1}$. Следовательно, $D = 4 \text{ м}^{-1}$.</p><p><strong>Найти:</strong></p><p>Фокусное расстояние $\text{F}$ — ?</p><p>Тип линзы — ?</p><p><strong>Решение:</strong></p><p>Оптическая сила линзы $\text{D}$ и ее фокусное расстояние $\text{F}$ связаны соотношением:</p><p>$D = \frac{1}{F}$</p><p>Выразим фокусное расстояние из этой формулы:</p><p>$F = \frac{1}{D}$</p><p>Подставим числовое значение оптической силы в единицах СИ:</p><p>$F = \frac{1}{4 \text{ м}^{-1}} = 0.25 \text{ м}$</p><p>Для наглядности можно перевести фокусное расстояние в сантиметры:</p><p>$F = 0.25 \text{ м} \cdot 100 \frac{\text{см}}{\text{м}} = 25 \text{ см}$</p><p>Тип линзы определяется знаком ее оптической силы. Поскольку оптическая сила $D = 4$ дптр — положительная величина ($D > 0$), то линза является <strong>собирающей</strong>.</p><p><strong>Ответ:</strong> Фокусное расстояние линзы равно $0.25$ м (или $\text{25}$ см). Линза является собирающей.</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" => "1428698" "type" => "task" ] "previous" => array:2 [ "refs" => "1428696" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1103 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1077 #items: array:1 [ 0 => App\Models\BookPage {#1076 #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" => 1428976 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/page-85" "field_display_title" => "85" "field_folder" => "1" "field_image_name" => "85" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1074 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1108 #items: array:1 [ 0 => App\Models\Book {#1119} ] #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 {#1107 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Element {#1159 #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" => 1683643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161 #items: array:1 [ 0 => App\Models\Edition {#1098} ] #escapeWhenCastingToString: false } "book_page" => array:2 [ "refs" => "1428976" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "85-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/85-1.webp?ts=1758964766" ] ] ] #original: array:6 [ "id" => 1683643 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1161} "book_page" => array:2 [ "refs" => "1428976" "type" => "book_page" ] "img" => array:1 [ 0 => array:5 [ "name" => "85-1.jpg" "alt" => null "width" => "1577" "height" => 2519 "path" => "/media/fizika_09/maron-dm/0-1/85-1.webp?ts=1758964766" ] ] ] #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" => "1428977" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1428975" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:4 [ 0 => App\Models\Task {#1264 #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" => 1428694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp14-9" "field_display_title" => "Вариант 9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1265 #items: [] #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 {#1266 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267 #items: array:1 [ 0 => App\Models\Branch {#1117} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1305 #items: array:2 [ 0 => App\Models\Branch {#1313 …30} 1 => App\Models\Branch {#1317 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1268 #items: array:2 [ 0 => App\Models\Element {#1296 …30} 1 => App\Models\Element {#1295 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428695" "type" => "task" ] "previous" => array:2 [ "refs" => "1428693" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1299 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428976" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428694 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp14-9" "field_display_title" => "Вариант 9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1265} "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 {#1266} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1267} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1305} "content" => Illuminate\Database\Eloquent\Collection {#1268} "next" => array:2 [ "refs" => "1428695" "type" => "task" ] "previous" => array:2 [ "refs" => "1428693" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1299} "page" => array:2 [ "refs" => "1428976" "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 {#1302 #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" => 1428695 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp14-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1310 #items: [] #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 {#1297 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300 #items: array:1 [ 0 => App\Models\Branch {#1313 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1269 #items: array:2 [ 0 => App\Models\Branch {#1313 …30} 1 => App\Models\Branch {#1317 …30} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1271 #items: array:2 [ 0 => App\Models\Element {#1285 …30} 1 => App\Models\Element {#1283 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428696" "type" => "task" ] "previous" => array:2 [ "refs" => "1428694" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428976" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428695 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp14-10" "field_display_title" => "Вариант 10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1310} "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 {#1297} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1300} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1269} "content" => Illuminate\Database\Eloquent\Collection {#1271} "next" => array:2 [ "refs" => "1428696" "type" => "task" ] "previous" => array:2 [ "refs" => "1428694" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1286} "page" => array:2 [ "refs" => "1428976" "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 {#1293 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1428696 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp15-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1301 #items: [] #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 {#1284 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289 #items: array:1 [ 0 => App\Models\Branch {#1313 …30} ] #escapeWhenCastingToString: false } "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290 #items: array:2 [ 0 => App\Models\Branch {#1313 …30} 1 => App\Models\Branch {#1151} ] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1291 #items: array:2 [ 0 => App\Models\Element {#1273 …30} 1 => App\Models\Element {#1304 …30} ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1428697" "type" => "task" ] "previous" => array:2 [ "refs" => "1428695" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1274 #items: array:1 [ 0 => App\Models\Book {#1119} ] #escapeWhenCastingToString: false } "page" => array:2 [ "refs" => "1428976" "type" => "book_page" ] ] #original: array:24 [ "id" => 1428696 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp15-1" "field_display_title" => "Вариант 1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1301} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1284} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1289} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1290} "content" => Illuminate\Database\Eloquent\Collection {#1291} "next" => array:2 [ "refs" => "1428697" "type" => "task" ] "previous" => array:2 [ "refs" => "1428695" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1274} "page" => array:2 [ "refs" => "1428976" "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 {#1278 #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" => 1428697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "85" "field_page_end" => null "field_url" => "/9-klass/fizika/maron-didakticheskie-materialy/cp15-2" "field_display_title" => "Вариант 2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1288 #items: [] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null 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[] #guarded: array:1 [ 0 => "*" ] }
Вариант 2 (с. 85)
Условие. Вариант 2 (с. 85)
скриншот условия
1. В каких случаях угол падения луча света на границу двух сред равен углу преломления?
2. Постройте изображение предмета AB в линзе (рис. 114). Охарактеризуйте изображение.
3. Оптическая сила линзы $D = 4 \text{ дптр}$. Чему равно фокусное расстояние этой линзы? Какая это линза?
Решение. Вариант 2 (с. 85)
1. В каких случаях угол падения луча света на границу двух сред равен углу преломления?
Угол падения луча света на границу двух сред равен углу преломления в двух случаях. Это следует из закона преломления света (закона Снеллиуса): $n_1 \sin \alpha = n_2 \sin \gamma$, где $n_1$ и $n_2$ — показатели преломления первой и второй сред, $\alpha$ — угол падения, а $\gamma$ — угол преломления.
Равенство $\alpha = \gamma$ возможно, если:
1. Луч света падает на границу раздела сред перпендикулярно. В этом случае угол падения $\alpha = 0^\circ$. Тогда из закона преломления следует, что и угол преломления $\gamma$ также будет равен $0^\circ$. Луч не меняет своего направления.
2. Показатели преломления двух сред одинаковы, то есть $n_1 = n_2$. В этом случае свет проходит через границу раздела так, как будто это однородная среда, и преломления не происходит. Для любого угла падения $\alpha$ угол преломления $\gamma$ будет ему равен.
Ответ: Угол падения равен углу преломления, если луч падает перпендикулярно на границу раздела двух сред или если показатели преломления этих сред одинаковы.
2. Постройте изображение предмета АВ в линзе (рис. 114). Охарактеризуйте изображение.
Так как рисунок 114 не предоставлен, построим изображение предмета АВ для общего случая, когда предмет находится между фокусом ($\text{F}$) и двойным фокусом ($\text{2F}$) собирающей линзы.
Для построения изображения точки B (вершины предмета) используем два луча с известным ходом:
• Луч, идущий от точки B параллельно главной оптической оси. После преломления в линзе он пройдет через ее задний фокус $F'$.
• Луч, идущий от точки B через оптический центр линзы O. Этот луч не преломляется и не меняет своего направления.
Точка B', где пересекутся эти два луча после прохождения через линзу, будет действительным изображением точки B. Опустив перпендикуляр из точки B' на главную оптическую ось, получим точку A' — изображение точки A. Таким образом, A'B' — это искомое изображение предмета АВ.
Характеристика полученного изображения A'B':
• Действительное, так как получено на пересечении самих преломленных лучей, а не их продолжений.
• Перевернутое, так как изображение направлено в противоположную сторону относительно главной оптической оси по сравнению с предметом.
• Увеличенное, так как его линейные размеры больше размеров предмета.
Ответ: Изображение, полученное в собирающей линзе для предмета, расположенного между фокусом и двойным фокусом, является действительным, перевернутым и увеличенным.
3. Оптическая сила линзы D = 4 дптр. Чему равно фокусное расстояние этой линзы? Какая это линза?
Дано:
Оптическая сила линзы $D = 4$ дптр.
Единица измерения оптической силы диоптрия (дптр) связана с основной единицей длины в СИ (метр) соотношением $1 \text{ дптр} = 1 \text{ м}^{-1}$. Следовательно, $D = 4 \text{ м}^{-1}$.
Найти:
Фокусное расстояние $\text{F}$ — ?
Тип линзы — ?
Решение:
Оптическая сила линзы $\text{D}$ и ее фокусное расстояние $\text{F}$ связаны соотношением:
$D = \frac{1}{F}$
Выразим фокусное расстояние из этой формулы:
$F = \frac{1}{D}$
Подставим числовое значение оптической силы в единицах СИ:
$F = \frac{1}{4 \text{ м}^{-1}} = 0.25 \text{ м}$
Для наглядности можно перевести фокусное расстояние в сантиметры:
$F = 0.25 \text{ м} \cdot 100 \frac{\text{см}}{\text{м}} = 25 \text{ см}$
Тип линзы определяется знаком ее оптической силы. Поскольку оптическая сила $D = 4$ дптр — положительная величина ($D > 0$), то линза является собирающей.
Ответ: Фокусное расстояние линзы равно $0.25$ м (или $\text{25}$ см). Линза является собирающей.
Другие задания:
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