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Номер 2, страница 298 - гдз по физике 9 класс учебник Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю.
Тип: Учебник
Серия: алгоритм успеха
Издательство: Вентана-граф
Год издания: 2012 - 2026
Цвет обложки: синий изображено здание и радуга
ISBN: 978-5-360-07412-0
Популярные ГДЗ в 9 классе
Глава 8. Оптика. Параграф 49. Построение изображений, создаваемых тонкими рассеивающими линзами. Упражнения - номер 2, страница 298.
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" => 1438518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49upr-2" "field_display_title" => "2" "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 {#1076 #items: array:1 [ 0 => App\Models\Branch {#1034 #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" => 1437978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039 #items: array:1 [ 0 => App\Models\Term {#1038 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "248" "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 {#1040 #items: array:1 [ 0 => App\Models\Book {#1041 #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" => 1202 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 1202 "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 {#1042 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1044 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1046 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1048 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1052 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1053 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1055 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1057 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1059 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1061 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1062 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1063 …2} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1065 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1067 …2} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1068 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1069 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1071 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1039} "field_page_start" => "248" "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 {#1040} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1073} ] #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 {#1155 #items: array:3 [ 0 => App\Models\Branch {#1165 #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" => 1437978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169 #items: array:1 [ 0 => App\Models\Term {#1166 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #original: array:7 [ "id" => 29 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Глава" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "248" "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 {#1202 #items: array:1 [ 0 => App\Models\Book {#1168 #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" => 1202 "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 {#1170 #items: array:1 [ 0 => App\Models\Term {#1167 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #original: array:10 [ "id" => 6493 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Физика" "field_abbreviated_name" => null "field_cases" => array:6 [ …6] "field_foreign_lang_name" => null "field_short_name" => null "field_subject_type" => "technical_subject" "field_translit" => "fizika" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1171 #items: array:1 [ 0 => App\Models\Term {#1172 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #original: array:6 [ "id" => 5458 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "9" "field_cases" => array:6 [ …6] "field_translit" => "devjatyj" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173 #items: array:1 [ 0 => App\Models\Term {#1174 #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" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #original: array:6 [ "id" => 5174 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вентана-граф" "field_cases" => null "field_translit" => "ventana-graf" ] #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 {#1175 #items: array:3 [ 0 => App\Models\Term {#1176 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 4180 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Грачев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Александр" "field_patronymic" => "Васильевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Term {#1177 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #original: array:12 [ "id" => 5484 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Погожев" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Владимир" "field_patronymic" => "Александрович" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Term {#1178 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1179 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1180 #items: array:1 [ 0 => App\Models\Term {#1181 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #original: array:10 [ "id" => 6671 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Учебник" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => null "field_short_name" => null "field_short_name_foreign" => null "field_translit" => "uchebnik" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1182 #items: array:1 [ 0 => App\Models\Term {#1183 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #original: array:6 [ "id" => 9 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Россия" "field_cases" => array:6 [ …6] "field_translit" => "rossiya" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1184 #items: array:1 [ 0 => App\Models\Term {#1185 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #original: array:6 [ "id" => 15 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Москва" "field_cases" => array:6 [ …6] "field_translit" => "moskva" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1186 #items: array:1 [ 0 => App\Models\Term {#1187 #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" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #original: array:8 [ "id" => 4697 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "алгоритм успеха" "field_cases" => null "field_foreign_lang_series" => null "field_transcription_eng" => null "field_translit" => "algoritm uspekha" ] #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 {#1188 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190 #items: array:1 [ 0 => App\Models\Term {#1191 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192 #items: array:1 [ 0 => App\Models\Term {#1193 #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" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #original: array:6 [ "id" => 6900 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "доработанное" "field_cases" => array:6 [ …6] "field_translit" => "dorabotannoe" ] #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 {#1194 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198 #items: array:1 [ 0 => App\Models\Term {#1199 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1202 "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 {#1170} "field_class" => Illuminate\Database\Eloquent\Collection {#1171} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1173} "field_author" => Illuminate\Database\Eloquent\Collection {#1175} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1179} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1180} "field_country" => Illuminate\Database\Eloquent\Collection {#1182} "field_city" => Illuminate\Database\Eloquent\Collection {#1184} "field_series" => Illuminate\Database\Eloquent\Collection {#1186} "field_umk" => Illuminate\Database\Eloquent\Collection {#1188} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1189} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1190} "field_publication_number" => "2" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1192} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1194} "field_under_the_edition_degree" => null "field_cover_description" => "изображено здание и радуга" "field_publication_year" => "2012" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для учащихся общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "580" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-u/" "field_isbn" => "978-5-360-07412-0" "field_cover" => array:1 [ 0 => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-u/covers/cover1.webp?ts=1759082140" "alt" => "" "width" => "2294" "height" => "3039" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1195} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1196} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1197} "field_url" => "/9-klass/fizika/grachev-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1198} "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 {#1200 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1437978 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1169} "field_page_start" => "248" "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 {#1202} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1200} ] #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 {#1201 #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" => 1438007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206 #items: array:1 [ 0 => App\Models\Term {#1203 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #original: array:7 [ "id" => 32 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Параграф" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => null "field_short_name" => "§" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "296" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1205 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1438007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1206} "field_page_start" => "296" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1205} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1204} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Branch {#1207 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1438009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1208 #items: [] #escapeWhenCastingToString: false } "field_page_start" => "298" "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 {#1209 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1254 #items: array:1 [ 0 => App\Models\Branch {#1210 #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" => 1438007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_page_start" => "296" "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 {#1213 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1246 …2} ] #original: array:24 [ "id" => 1438007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Построение изображений, создаваемых тонкими рассеивающими линзами" "field_branch_order" => "49" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1212 …2} "field_page_start" => "296" "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 {#1213 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1246 …2} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1438009 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Упражнения" "field_branch_order" => null "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1208} "field_page_start" => "298" "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 {#1209} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1254} ] #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 {#1112 #items: array:2 [ 0 => App\Models\Element {#1144 #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" => 1705402 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134 #items: array:1 [ 0 => App\Models\Edition {#1143 #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" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6112 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1140 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1138 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1139 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1438518" "type" => "task" ] "text" => "<p><strong>2.</strong> Постройте изображение светящейся точки, расположенной перед рассеивающей линзой ($F = -6 \text{ см}$) на расстоянии $a = 4 \text{ см}$ от её главной плоскости и на расстоянии $h = 2 \text{ см}$ от её главной оптической оси.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "484" "height" => 123 "path" => "/media/fizika_09/grachev-u/0-49upr/2-1.webp?ts=1759503227" ] ] ] #original: array:7 [ "id" => 1705402 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1134} "task" => array:2 [ "refs" => "1438518" "type" => "task" ] "text" => "<p><strong>2.</strong> Постройте изображение светящейся точки, расположенной перед рассеивающей линзой ($F = -6 \text{ см}$) на расстоянии $a = 4 \text{ см}$ от её главной плоскости и на расстоянии $h = 2 \text{ см}$ от её главной оптической оси.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "2-1.jpg" "alt" => null "width" => "484" "height" => 123 "path" => "/media/fizika_09/grachev-u/0-49upr/2-1.webp?ts=1759503227" ] ] ] #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 {#1137 #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" => 1813086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1127 #items: array:1 [ 0 => App\Models\Edition {#1136 #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" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6644 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1132 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1130 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1131 …2} "field_content_source" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "task" => array:2 [ "refs" => "1438518" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Тип линзы: рассеивающая<br>Фокусное расстояние, $F = -6$ см<br>Расстояние от точки до линзы, $a = 4$ см<br>Высота точки над главной оптической осью, $h = 2$ см</p><p>В системе СИ:<br>$F = -0.06$ м<br>$a = 0.04$ м<br>$h = 0.02$ м</p><p><strong>Найти:</strong></p><p>Построить изображение точки и найти его характеристики: расстояние от линзы $\text{b}$ и высоту $h'$.</p><p><strong>Решение:</strong></p><p>Решение задачи можно провести двумя способами: аналитическим (с помощью формул) и графическим (построением). Для полноты ответа приведем оба способа.</p><p><em>1. Аналитический расчет</em></p><p>Для определения положения изображения воспользуемся формулой тонкой линзы:$$ \frac{1}{a} + \frac{1}{b} = \frac{1}{F} $$где $\text{a}$ – расстояние от предмета до линзы, $\text{b}$ – расстояние от изображения до линзы, $\text{F}$ – фокусное расстояние. Для рассеивающей линзы фокусное расстояние является отрицательной величиной ($F < 0$).</p><p>Выразим из формулы искомую величину $\text{b}$:$$ \frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{a - F}{aF} $$$$ b = \frac{aF}{a - F} $$Подставим числовые значения из условия задачи (для удобства используем сантиметры):$$ b = \frac{4 \text{ см} \cdot (-6 \text{ см})}{4 \text{ см} - (-6 \text{ см})} = \frac{-24 \text{ см}^2}{10 \text{ см}} = -2.4 \text{ см} $$Знак «минус» у величины $\text{b}$ указывает на то, что изображение является <em>мнимым</em> и расположено с той же стороны от линзы, что и сама светящаяся точка. Расстояние от изображения до линзы составляет 2.4 см.</p><p>Далее найдем высоту изображения $h'$ с помощью формулы линейного увеличения линзы $\Gamma$:$$ \Gamma = \frac{h'}{h} = -\frac{b}{a} $$где $\text{h}$ – высота предмета (в данном случае, расстояние от точки до главной оптической оси), $h'$ – высота изображения.</p><p>Выразим $h'$ из этой формулы:$$ h' = h \cdot \left(-\frac{b}{a}\right) $$Подставим известные значения:$$ h' = 2 \text{ см} \cdot \left(-\frac{-2.4 \text{ см}}{4 \text{ см}}\right) = 2 \text{ см} \cdot \frac{2.4}{4} = 2 \text{ см} \cdot 0.6 = 1.2 \text{ см} $$Положительное значение $h'$ означает, что изображение <em>прямое</em> (неперевернутое). Поскольку $|h'| < |h|$ (1.2 см < 2 см), изображение является <em>уменьшенным</em>.</p><p><em>2. Геометрическое построение</em></p><p>Для построения изображения светящейся точки S в рассеивающей линзе необходимо провести как минимум два из трех «удобных» лучей:<br>1. Луч, параллельный главной оптической оси. После преломления в линзе он пойдет так, как будто вышел из переднего (мнимого) фокуса F.<br>2. Луч, проходящий через оптический центр линзы O. Такой луч не претерпевает преломления.</p><p>Изображение точки S' будет находиться в точке пересечения продолжения первого преломленного луча и второго луча.</p><svg width="500" height="300" viewBox="-75 -50 95 100" xmlns="http://www.w3.org/2000/svg" style="background-color: #f9f9f9; border: 1px solid #ccc;"><defs><pattern id="grid" width="10" height="10" patternUnits="userSpaceOnUse"><path d="M 10 0 L 0 0 0 10" fill="none" stroke="#e0e0e0" stroke-width="1"></path></pattern><marker id="arrowhead-red" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="red"></path></marker><marker id="arrowhead-green" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="green"></path></marker></defs><rect width="100%" height="100%" fill="url(#grid)"></rect><!-- Axis --><line x1="-75" y1="0" x2="95" y2="0" stroke="black" stroke-width="1.5"></line><!-- Lens --><line x1="0" y1="-40" x2="0" y2="40" stroke="black" stroke-width="1.5"></line><path d="M 0 -40 L -5 -45 M 0 -40 L 5 -45 M 0 40 L -5 45 M 0 40 L 5 45" stroke="black" stroke-width="1.5" fill="none"></path><!-- Foci and Center --><circle cx="-60" cy="0" r="1.5" fill="black"></circle><text x="-65" y="-5" font-family="Verdana" font-size="10">F</text><circle cx="60" cy="0" r="1.5" fill="black"></circle><text x="55" y="-5" font-family="Verdana" font-size="10">F'</text><circle cx="0" cy="0" r="1.5" fill="black"></circle><text x="2" y="-5" font-family="Verdana" font-size="10">O</text><!-- Object Point S --><circle cx="-40" cy="20" r="2" fill="blue"></circle><text x="-45" y="28" font-family="Verdana" font-size="12" fill="blue">S</text><!-- Ray 1 --><line x1="-40" y1="20" x2="-2" y2="20" stroke="red" stroke-width="1" marker-end="url(#arrowhead-red)"></line><line x1="0" y1="20" x2="38" y2="32.67" stroke="red" stroke-width="1" marker-end="url(#arrowhead-red)"></line><line x1="-60" y1="0" x2="0" y2="20" stroke="red" stroke-width="1" stroke-dasharray="3,3"></line><!-- Ray 2 --><line x1="-40" y1="20" x2="28" y2="-14" stroke="green" stroke-width="1" marker-end="url(#arrowhead-green)"></line><!-- Image Point S' --><circle cx="-24" cy="12" r="2" fill="#9400D3"></circle><text x="-32" y="10" font-family="Verdana" font-size="12" fill="#9400D3">S'</text></svg><p>На графике, построенном в масштабе (1 клетка = 1 см), видно, что координаты изображения S' примерно (-2.4 см; 1.2 см), что полностью совпадает с результатами аналитического расчета.</p><p><strong>Ответ:</strong></p><p>Изображение светящейся точки S' является мнимым, прямым и уменьшенным. Оно расположено на расстоянии $b = 2.4$ см от главной плоскости линзы (с той же стороны, что и точка S) и на высоте $h' = 1.2$ см над главной оптической осью.</p>" ] #original: array:6 [ "id" => 1813086 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1127} "task" => array:2 [ "refs" => "1438518" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p><p>Тип линзы: рассеивающая<br>Фокусное расстояние, $F = -6$ см<br>Расстояние от точки до линзы, $a = 4$ см<br>Высота точки над главной оптической осью, $h = 2$ см</p><p>В системе СИ:<br>$F = -0.06$ м<br>$a = 0.04$ м<br>$h = 0.02$ м</p><p><strong>Найти:</strong></p><p>Построить изображение точки и найти его характеристики: расстояние от линзы $\text{b}$ и высоту $h'$.</p><p><strong>Решение:</strong></p><p>Решение задачи можно провести двумя способами: аналитическим (с помощью формул) и графическим (построением). Для полноты ответа приведем оба способа.</p><p><em>1. Аналитический расчет</em></p><p>Для определения положения изображения воспользуемся формулой тонкой линзы:$$ \frac{1}{a} + \frac{1}{b} = \frac{1}{F} $$где $\text{a}$ – расстояние от предмета до линзы, $\text{b}$ – расстояние от изображения до линзы, $\text{F}$ – фокусное расстояние. Для рассеивающей линзы фокусное расстояние является отрицательной величиной ($F < 0$).</p><p>Выразим из формулы искомую величину $\text{b}$:$$ \frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{a - F}{aF} $$$$ b = \frac{aF}{a - F} $$Подставим числовые значения из условия задачи (для удобства используем сантиметры):$$ b = \frac{4 \text{ см} \cdot (-6 \text{ см})}{4 \text{ см} - (-6 \text{ см})} = \frac{-24 \text{ см}^2}{10 \text{ см}} = -2.4 \text{ см} $$Знак «минус» у величины $\text{b}$ указывает на то, что изображение является <em>мнимым</em> и расположено с той же стороны от линзы, что и сама светящаяся точка. Расстояние от изображения до линзы составляет 2.4 см.</p><p>Далее найдем высоту изображения $h'$ с помощью формулы линейного увеличения линзы $\Gamma$:$$ \Gamma = \frac{h'}{h} = -\frac{b}{a} $$где $\text{h}$ – высота предмета (в данном случае, расстояние от точки до главной оптической оси), $h'$ – высота изображения.</p><p>Выразим $h'$ из этой формулы:$$ h' = h \cdot \left(-\frac{b}{a}\right) $$Подставим известные значения:$$ h' = 2 \text{ см} \cdot \left(-\frac{-2.4 \text{ см}}{4 \text{ см}}\right) = 2 \text{ см} \cdot \frac{2.4}{4} = 2 \text{ см} \cdot 0.6 = 1.2 \text{ см} $$Положительное значение $h'$ означает, что изображение <em>прямое</em> (неперевернутое). Поскольку $|h'| < |h|$ (1.2 см < 2 см), изображение является <em>уменьшенным</em>.</p><p><em>2. Геометрическое построение</em></p><p>Для построения изображения светящейся точки S в рассеивающей линзе необходимо провести как минимум два из трех «удобных» лучей:<br>1. Луч, параллельный главной оптической оси. После преломления в линзе он пойдет так, как будто вышел из переднего (мнимого) фокуса F.<br>2. Луч, проходящий через оптический центр линзы O. Такой луч не претерпевает преломления.</p><p>Изображение точки S' будет находиться в точке пересечения продолжения первого преломленного луча и второго луча.</p><svg width="500" height="300" viewBox="-75 -50 95 100" xmlns="http://www.w3.org/2000/svg" style="background-color: #f9f9f9; border: 1px solid #ccc;"><defs><pattern id="grid" width="10" height="10" patternUnits="userSpaceOnUse"><path d="M 10 0 L 0 0 0 10" fill="none" stroke="#e0e0e0" stroke-width="1"></path></pattern><marker id="arrowhead-red" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="red"></path></marker><marker id="arrowhead-green" viewBox="0 0 10 10" refX="8" refY="5" markerWidth="6" markerHeight="6" orient="auto-start-reverse"><path d="M 0 0 L 10 5 L 0 10 z" fill="green"></path></marker></defs><rect width="100%" height="100%" fill="url(#grid)"></rect><!-- Axis --><line x1="-75" y1="0" x2="95" y2="0" stroke="black" stroke-width="1.5"></line><!-- Lens --><line x1="0" y1="-40" x2="0" y2="40" stroke="black" stroke-width="1.5"></line><path d="M 0 -40 L -5 -45 M 0 -40 L 5 -45 M 0 40 L -5 45 M 0 40 L 5 45" stroke="black" stroke-width="1.5" fill="none"></path><!-- Foci and Center --><circle cx="-60" cy="0" r="1.5" fill="black"></circle><text x="-65" y="-5" font-family="Verdana" font-size="10">F</text><circle cx="60" cy="0" r="1.5" fill="black"></circle><text x="55" y="-5" font-family="Verdana" font-size="10">F'</text><circle cx="0" cy="0" r="1.5" fill="black"></circle><text x="2" y="-5" font-family="Verdana" font-size="10">O</text><!-- Object Point S --><circle cx="-40" cy="20" r="2" fill="blue"></circle><text x="-45" y="28" font-family="Verdana" font-size="12" fill="blue">S</text><!-- Ray 1 --><line x1="-40" y1="20" x2="-2" y2="20" stroke="red" stroke-width="1" marker-end="url(#arrowhead-red)"></line><line x1="0" y1="20" x2="38" y2="32.67" stroke="red" stroke-width="1" marker-end="url(#arrowhead-red)"></line><line x1="-60" y1="0" x2="0" y2="20" stroke="red" stroke-width="1" stroke-dasharray="3,3"></line><!-- Ray 2 --><line x1="-40" y1="20" x2="28" y2="-14" stroke="green" stroke-width="1" marker-end="url(#arrowhead-green)"></line><!-- Image Point S' --><circle cx="-24" cy="12" r="2" fill="#9400D3"></circle><text x="-32" y="10" font-family="Verdana" font-size="12" fill="#9400D3">S'</text></svg><p>На графике, построенном в масштабе (1 клетка = 1 см), видно, что координаты изображения S' примерно (-2.4 см; 1.2 см), что полностью совпадает с результатами аналитического расчета.</p><p><strong>Ответ:</strong></p><p>Изображение светящейся точки S' является мнимым, прямым и уменьшенным. Оно расположено на расстоянии $b = 2.4$ см от главной плоскости линзы (с той же стороны, что и точка S) и на высоте $h' = 1.2$ см над главной оптической осью.</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" => "1438519" "type" => "task" ] "previous" => array:2 [ "refs" => "1438517" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1168} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\BookPage {#1116 #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" => 1437804 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-298" "field_display_title" => "298" "field_folder" => "1" "field_image_name" => "298" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1129 #items: array:1 [ 0 => App\Models\Book {#1168} ] #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 {#1123 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Element {#1118 #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" => 1705800 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1151 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1705800 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1151 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "next" => array:2 [ "refs" => "1437805" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437803" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1349 #items: array:8 [ 0 => App\Models\Task {#1363 #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" => 1438513 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1364 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1365 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1366 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1525 …2} "content" => Illuminate\Database\Eloquent\Collection {#1524 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1532 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438513 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-1" "field_display_title" => "1" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1364 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1365 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1366 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1525 …2} "content" => Illuminate\Database\Eloquent\Collection {#1524 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1532 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 1 => App\Models\Task {#1527 #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" => 1438514 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1526 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1534 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1530 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1528 …2} "content" => Illuminate\Database\Eloquent\Collection {#1547 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1552 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438514 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1526 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1534 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1530 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1528 …2} "content" => Illuminate\Database\Eloquent\Collection {#1547 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1552 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 2 => App\Models\Task {#1531 #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" => 1438515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1539 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1529 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1544 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1543 …2} "content" => Illuminate\Database\Eloquent\Collection {#1559 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1564 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1438515 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1539 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1529 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1544 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1543 …2} "content" => Illuminate\Database\Eloquent\Collection {#1559 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1564 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Task {#1542 #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" => 1438516 "created_at" => "2026-04-10 13:58:26" "updated_at" => null 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=> null "field_url" => "/9-klass/fizika/grachev-uchebnik/49vopr-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1541 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] "edition_groups" => Illuminate\Database\Eloquent\Collection {#1540 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1548 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1550 …2} "content" => Illuminate\Database\Eloquent\Collection {#1546 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1560 …2} "page" => array:2 [ …2] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 4 => App\Models\Task {#1545 #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" => 1438517 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49upr-1" …18 ] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 5 => App\Models\Task {#1575 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 6 => App\Models\Task {#1587 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } 7 => App\Models\Task {#1594 #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 [ …24] #original: array:24 [ …24] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ …1] } ] #escapeWhenCastingToString: false } ] #original: array:21 [ "id" => 1437804 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_url" => "/9-klass/fizika/grachev-uchebnik/page-298" "field_display_title" => "298" "field_folder" => "1" "field_image_name" => "298" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1128} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1129} "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 {#1123} "content" => Illuminate\Database\Eloquent\Collection {#1150} "next" => array:2 [ "refs" => "1437805" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1437803" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1349} ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1438518 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "298" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-uchebnik/49upr-2" "field_display_title" => "2" "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 {#1076} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1155} "content" => Illuminate\Database\Eloquent\Collection {#1112} "next" => array:2 [ "refs" => "1438519" "type" => "task" ] "previous" => array:2 [ "refs" => "1438517" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146} "page" => array:2 [ "refs" => "1437804" "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 (с. 298)
Условие. №2 (с. 298)
скриншот условия
2. Постройте изображение светящейся точки, расположенной перед рассеивающей линзой ($F = -6 \text{ см}$) на расстоянии $a = 4 \text{ см}$ от её главной плоскости и на расстоянии $h = 2 \text{ см}$ от её главной оптической оси.
Решение. №2 (с. 298)
Дано:
Тип линзы: рассеивающая
Фокусное расстояние, $F = -6$ см
Расстояние от точки до линзы, $a = 4$ см
Высота точки над главной оптической осью, $h = 2$ см
В системе СИ:
$F = -0.06$ м
$a = 0.04$ м
$h = 0.02$ м
Найти:
Построить изображение точки и найти его характеристики: расстояние от линзы $\text{b}$ и высоту $h'$.
Решение:
Решение задачи можно провести двумя способами: аналитическим (с помощью формул) и графическим (построением). Для полноты ответа приведем оба способа.
1. Аналитический расчет
Для определения положения изображения воспользуемся формулой тонкой линзы:$$ \frac{1}{a} + \frac{1}{b} = \frac{1}{F} $$где $\text{a}$ – расстояние от предмета до линзы, $\text{b}$ – расстояние от изображения до линзы, $\text{F}$ – фокусное расстояние. Для рассеивающей линзы фокусное расстояние является отрицательной величиной ($F < 0$).
Выразим из формулы искомую величину $\text{b}$:$$ \frac{1}{b} = \frac{1}{F} - \frac{1}{a} = \frac{a - F}{aF} $$$$ b = \frac{aF}{a - F} $$Подставим числовые значения из условия задачи (для удобства используем сантиметры):$$ b = \frac{4 \text{ см} \cdot (-6 \text{ см})}{4 \text{ см} - (-6 \text{ см})} = \frac{-24 \text{ см}^2}{10 \text{ см}} = -2.4 \text{ см} $$Знак «минус» у величины $\text{b}$ указывает на то, что изображение является мнимым и расположено с той же стороны от линзы, что и сама светящаяся точка. Расстояние от изображения до линзы составляет 2.4 см.
Далее найдем высоту изображения $h'$ с помощью формулы линейного увеличения линзы $\Gamma$:$$ \Gamma = \frac{h'}{h} = -\frac{b}{a} $$где $\text{h}$ – высота предмета (в данном случае, расстояние от точки до главной оптической оси), $h'$ – высота изображения.
Выразим $h'$ из этой формулы:$$ h' = h \cdot \left(-\frac{b}{a}\right) $$Подставим известные значения:$$ h' = 2 \text{ см} \cdot \left(-\frac{-2.4 \text{ см}}{4 \text{ см}}\right) = 2 \text{ см} \cdot \frac{2.4}{4} = 2 \text{ см} \cdot 0.6 = 1.2 \text{ см} $$Положительное значение $h'$ означает, что изображение прямое (неперевернутое). Поскольку $|h'| < |h|$ (1.2 см < 2 см), изображение является уменьшенным.
2. Геометрическое построение
Для построения изображения светящейся точки S в рассеивающей линзе необходимо провести как минимум два из трех «удобных» лучей:
1. Луч, параллельный главной оптической оси. После преломления в линзе он пойдет так, как будто вышел из переднего (мнимого) фокуса F.
2. Луч, проходящий через оптический центр линзы O. Такой луч не претерпевает преломления.
Изображение точки S' будет находиться в точке пересечения продолжения первого преломленного луча и второго луча.
На графике, построенном в масштабе (1 клетка = 1 см), видно, что координаты изображения S' примерно (-2.4 см; 1.2 см), что полностью совпадает с результатами аналитического расчета.
Ответ:
Изображение светящейся точки S' является мнимым, прямым и уменьшенным. Оно расположено на расстоянии $b = 2.4$ см от главной плоскости линзы (с той же стороны, что и точка S) и на высоте $h' = 1.2$ см над главной оптической осью.
Другие задания:
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