gdz.top
Номер 4, страница 58, часть 3 - гдз по физике 9 класс рабочая тетрадь Грачев, Погожев
Авторы: Грачев А. В., Погожев В. А., Боков П. Ю., Вишнякова Е. А.
Тип: рабочая тетрадь
Издательство: Просвещение
Год издания: 2021 - 2026
Часть: 3
Цвет обложки: синий
ISBN: 978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)
Популярные ГДЗ в 9 классе
Часть 3. Глава 8. Оптика. Параграф 51. Границы применимости законов геометрической оптики. Интерференция. Дифракция - номер 4, страница 58.
App\Models\Task {#1003 // 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" => 1435353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1009 #items: array:1 [ 0 => App\Models\Term {#1008 #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 {#1007 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1048 #items: array:1 [ 0 => App\Models\Branch {#1006 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1011 #items: array:1 [ 0 => App\Models\Term {#1010 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1012 #items: array:1 [ 0 => App\Models\Book {#1013 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1014 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1016 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1018 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1020 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1025 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1026 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1028 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1030 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1032 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1033 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1043 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ …3] ] #original: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1014 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1016 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1018 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1020 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1025 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1026 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1028 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1030 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1032 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1033 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1034 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1035 …2} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1037 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1039 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ …3] "field_cover_alts" => array:3 [ …3] "field_covers" => array:3 [ …3] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1040 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1041 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1042 …2} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1043 …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 {#1045 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1011} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1012} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1045} ] #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 {#1127 #items: array:3 [ 0 => App\Models\Branch {#1137 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141 #items: array:1 [ 0 => App\Models\Term {#1138 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #original: array:7 [ "id" => 31 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Часть" "field_cases" => array:6 [ …6] "field_page_check_not_needed" => "1" "field_short_name" => "ч." ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1174 #items: array:1 [ 0 => App\Models\Book {#1140 #connection: "mysql" #table: "books" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1142 #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: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 {#1143 #items: array:1 [ 0 => App\Models\Term {#1144 #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 {#1145 #items: array:1 [ 0 => App\Models\Term {#1146 #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 {#1147 #items: array:4 [ 0 => App\Models\Term {#1148 #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 {#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: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 {#1150 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #original: array:12 [ "id" => 3888 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Боков" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Павел" "field_patronymic" => "Юрьевич" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } 3 => App\Models\Term {#1151 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #original: array:12 [ "id" => 4007 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "Вишнякова" "field_bio" => null "field_degree_rp" => null "field_foreign_lang_name" => null "field_foreign_lang_patronymic" => null "field_foreign_lang_surname" => null "field_name" => "Екатерина" "field_patronymic" => "Анатольевна" "field_surname_rp" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1152 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1153 #items: array:1 [ 0 => App\Models\Term {#1154 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #original: array:10 [ "id" => 6736 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "рабочая тетрадь" "field_book_type_foreign" => null "field_cases" => array:6 [ …6] "field_plural_form" => "рабочие тетради" "field_short_name" => "рт" "field_short_name_foreign" => null "field_translit" => "rabochaya tetrad" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1155 #items: array:1 [ 0 => App\Models\Term {#1156 #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 {#1157 #items: array:1 [ 0 => App\Models\Term {#1158 #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 {#1159 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1160 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1161 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1162 #items: array:1 [ 0 => App\Models\Term {#1163 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #original: array:10 [ "id" => 6706 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "ФГОС (старый)" "field_cases" => array:6 [ …6] "field_color" => null "field_end_year" => "2022" "field_start_year" => "2019" "field_translit" => "fgos-old" "field_type" => null ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1164 #items: array:1 [ 0 => App\Models\Term {#1165 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #original: array:6 [ "id" => 33 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "стереотипное" "field_cases" => array:6 [ …6] "field_translit" => "stereotipnoe" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1166 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1167 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1168 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1169 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1170 #items: array:1 [ 0 => App\Models\Term {#1171 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #original: array:6 [ "id" => 49 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "name" => "синий" "field_cases" => array:6 [ …6] "field_translit" => "siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 380 "subject" => 556 "class_subject" => 493 ] ] #original: array:50 [ "id" => 1203 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" => null "field_subject" => Illuminate\Database\Eloquent\Collection {#1142} "field_class" => Illuminate\Database\Eloquent\Collection {#1143} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1145} "field_author" => Illuminate\Database\Eloquent\Collection {#1147} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1152} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1153} "field_country" => Illuminate\Database\Eloquent\Collection {#1155} "field_city" => Illuminate\Database\Eloquent\Collection {#1157} "field_series" => Illuminate\Database\Eloquent\Collection {#1159} "field_umk" => Illuminate\Database\Eloquent\Collection {#1160} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1161} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1162} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1164} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1166} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2021" "field_publication_year_until" => null "field_part" => "1, 2, 3" "field_part_writing" => "Часть" "field_second_foreign_language" => null "field_for_whom" => "Учебное издание" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "594" "field_priority" => null "field_default_folder" => "/fizika_09/grachev-rt/" "field_isbn" => "978-5-09-098826-1 (ч.1) 978-5-09-098880-3 (ч.2) 978-5-09-098881-0 (ч.3)" "field_cover" => array:3 [ 0 => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" 1 => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" 2 => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" ] "field_cover_alts" => array:3 [ 0 => "" 1 => "" 2 => "" ] "field_covers" => array:3 [ 0 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover1.webp?ts=1759003248" "alt" => "" "width" => "2293" "height" => "2989" ] 1 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover2.webp?ts=1759003248" "alt" => "" "width" => "2265" "height" => "3003" ] 2 => array:4 [ "path" => "/media/fizika_09/grachev-rt/covers/cover3.webp?ts=1759003248" "alt" => "" "width" => "2241" "height" => "2999" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1167} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1168} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1169} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1170} "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 {#1172 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434847 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => null "field_branch_order" => "3" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1141} "field_page_start" => "3" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1174} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1172} ] #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 {#1173 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178 #items: array:1 [ 0 => App\Models\Term {#1175 #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" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1177 #items: array:1 [ 0 => App\Models\Book {#1140} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1176 #items: array:1 [ 0 => App\Models\Branch {#1006} ] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1178} "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1177} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1176} ] #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 {#1179 #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" => 1434865 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Границы применимости законов геометрической оптики. Интерференция. Дифракция" "field_branch_order" => "51" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Term {#1180 #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" => "57" "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 {#1182 #items: array:1 [ 0 => App\Models\Book {#1140} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227 #items: array:1 [ 0 => App\Models\Branch {#1181 #connection: "mysql" #table: "branches" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1219 …2} ] #original: array:24 [ "id" => 1434852 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Оптика" "field_branch_order" => "8" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1185 …2} "field_page_start" => "15" "field_branch_display" => "0" "field_branch_expanded" => "0" "field_display_branch_in_title" => "1" "field_display_task_interval" => "0" "field_display_branch_page" => "1" "field_branch_title_in_content" => "0" "field_navigation_title" => null "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_branch_cover" => [] "field_branch_covers" => [] "book" => Illuminate\Database\Eloquent\Collection {#1186 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1219 …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" => 1434865 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Границы применимости законов геометрической оптики. Интерференция. Дифракция" "field_branch_order" => "51" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1183} "field_page_start" => "57" "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 {#1182} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1227} ] #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 {#1084 #items: array:2 [ 0 => App\Models\Element {#1116 #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" => 1698741 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1105 #items: array:1 [ 0 => App\Models\Edition {#1107 #connection: "mysql" #table: "editions" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1102 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6173 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1101 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1099 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1103 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1102 …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" => "1435353" "type" => "task" ] "text" => "<p><strong>4.</strong> Изобразите ход волн в опыте Юнга. Обозначьте на рисунке разность хода волн.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1841" "height" => 243 "path" => "/media/fizika_09/grachev-rt/0-51/4-1.webp?ts=1759402888" ] ] ] #original: array:7 [ "id" => 1698741 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1105} "task" => array:2 [ "refs" => "1435353" "type" => "task" ] "text" => "<p><strong>4.</strong> Изобразите ход волн в опыте Юнга. Обозначьте на рисунке разность хода волн.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "4-1.jpg" "alt" => null "width" => "1841" "height" => 243 "path" => "/media/fizika_09/grachev-rt/0-51/4-1.webp?ts=1759402888" ] ] ] #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 {#1114 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1734727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095 #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" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6327 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => null "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1122 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1096 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1092 …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" => "1435353" "type" => "task" ] "text" => "<p><strong>Решение:</strong></p><p>Опыт Юнга — это классический эксперимент, демонстрирующий явление интерференции света и доказывающий его волновую природу. В этом опыте когерентный свет (например, от лазера) проходит через две близко расположенные щели и создает на удаленном экране интерференционную картину в виде чередующихся светлых и темных полос.</p><p>Схема опыта, иллюстрирующая ход волн и разность хода, представлена на рисунке ниже.</p><svg width="450" height="250" xmlns="http://www.w3.org/2000/svg" style="display: block; margin: 20px 0;"> <line x1="50" y1="20" x2="50" y2="105" stroke="black" stroke-width="4"></line> <line x1="50" y1="145" x2="50" y2="230" stroke="black" stroke-width="4"></line> <text x="25" y="120" font-family="sans-serif" font-size="16">S₁</text> <text x="25" y="140" font-family="sans-serif" font-size="16">S₂</text> <line x1="400" y1="0" x2="400" y2="250" stroke="gray" stroke-width="2"></line> <text x="405" y="20" font-family="sans-serif" font-size="14">Экран</text> <circle cx="400" cy="180" r="3" fill="red"></circle> <text x="410" y="185" font-family="sans-serif" font-size="16">P</text> <line x1="50" y1="125" x2="400" y2="125" stroke="black" stroke-width="1" stroke-dasharray="5,5"></line> <text x="220" y="120" font-family="sans-serif" font-size="16">L</text> <line x1="50" y1="115" x2="400" y2="180" stroke="blue" stroke-width="1.5"></line> <text x="220" y="140" font-family="sans-serif" font-size="16">r₁</text> <line x1="50" y1="135" x2="400" y2="180" stroke="green" stroke-width="1.5"></line> <text x="220" y="165" font-family="sans-serif" font-size="16">r₂</text> <path d="M 50 135 L 53.0 115.6" stroke="red" stroke-width="2"></path> <path d="M 50 115 L 53.0 115.6" stroke="red" stroke-width="1"></path> <text x="55" y="135" font-family="sans-serif" font-size="16" fill="red">Δr</text> <line x1="50" y1="125" x2="400" y2="180" stroke="purple" stroke-width="1" stroke-dasharray="3,3"></line> <path d="M 80 125 A 30 30 0 0 1 78.4 133.8" stroke="purple" fill="none"></path> <text x="85" y="135" font-family="sans-serif" font-size="16" fill="purple">θ</text> <line x1="40" y1="115" x2="40" y2="135" stroke="black" stroke-width="1"></line> <text x="20" y="130" font-family="sans-serif" font-size="16">d</text></svg><p> На рисунке обозначены:<br> $S_1$ и $S_2$ — две узкие щели, которые по принципу Гюйгенса-Френеля становятся когерентными источниками вторичных волн.<br> $d$ — расстояние между центрами щелей.<br> $L$ — расстояние от экрана со щелями до наблюдательного экрана.<br> $P$ — произвольная точка на экране, в которой наблюдается результат интерференции.<br> $r_1$ и $r_2$ — расстояния (пути), проходимые волнами от щелей $S_1$ и $S_2$ до точки $P$ соответственно.<br> $\theta$ — угол, под которым видна точка $P$ из середины отрезка, соединяющего щели.</p><p>Ключевой величиной, определяющей результат интерференции в точке $P$, является <strong>разность хода волн</strong>. Это разница в расстояниях, которые проходят волны от источников $S_1$ и $S_2$ до точки $P$. Она обозначается как $\Delta r$ и равна:</p><p>$\Delta r = r_2 - r_1$</p><p>На рисунке разность хода $\Delta r$ схематически показана красным отрезком. В приближении, когда расстояние до экрана $L$ значительно больше расстояния между щелями $d$ ($L \gg d$), разность хода можно с хорошей точностью вычислить по геометрической формуле:</p><p>$\Delta r = d \sin\theta$</p><p>Результат интерференции зависит от того, как разность хода соотносится с длиной волны света $\lambda$:<br> <strong>Условие максимума (светлая полоса):</strong> волны приходят в точку $P$ в одной фазе и усиливают друг друга. Это происходит, когда разность хода равна целому числу длин волн.<br> $\Delta r = m \lambda$, где $m = 0, \pm1, \pm2, ...$<br><br> <strong>Условие минимума (темная полоса):</strong> волны приходят в точку $P$ в противофазе и гасят друг друга. Это происходит, когда разность хода равна полуцелому числу длин волн.<br> $\Delta r = (m + \frac{1}{2}) \lambda$, где $m = 0, \pm1, \pm2, ...$</p><p><strong>Ответ:</strong> Схема опыта Юнга с изображением хода волн и обозначением разности хода представлена на рисунке и в пояснениях выше. Разность хода волн — это разница расстояний $\Delta r = r_2 - r_1$, которая для данного эксперимента может быть найдена по формуле $\Delta r = d \sin\theta$.</p>" ] #original: array:6 [ "id" => 1734727 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1095} "task" => array:2 [ "refs" => "1435353" "type" => "task" ] "text" => "<p><strong>Решение:</strong></p><p>Опыт Юнга — это классический эксперимент, демонстрирующий явление интерференции света и доказывающий его волновую природу. В этом опыте когерентный свет (например, от лазера) проходит через две близко расположенные щели и создает на удаленном экране интерференционную картину в виде чередующихся светлых и темных полос.</p><p>Схема опыта, иллюстрирующая ход волн и разность хода, представлена на рисунке ниже.</p><svg width="450" height="250" xmlns="http://www.w3.org/2000/svg" style="display: block; margin: 20px 0;"> <line x1="50" y1="20" x2="50" y2="105" stroke="black" stroke-width="4"></line> <line x1="50" y1="145" x2="50" y2="230" stroke="black" stroke-width="4"></line> <text x="25" y="120" font-family="sans-serif" font-size="16">S₁</text> <text x="25" y="140" font-family="sans-serif" font-size="16">S₂</text> <line x1="400" y1="0" x2="400" y2="250" stroke="gray" stroke-width="2"></line> <text x="405" y="20" font-family="sans-serif" font-size="14">Экран</text> <circle cx="400" cy="180" r="3" fill="red"></circle> <text x="410" y="185" font-family="sans-serif" font-size="16">P</text> <line x1="50" y1="125" x2="400" y2="125" stroke="black" stroke-width="1" stroke-dasharray="5,5"></line> <text x="220" y="120" font-family="sans-serif" font-size="16">L</text> <line x1="50" y1="115" x2="400" y2="180" stroke="blue" stroke-width="1.5"></line> <text x="220" y="140" font-family="sans-serif" font-size="16">r₁</text> <line x1="50" y1="135" x2="400" y2="180" stroke="green" stroke-width="1.5"></line> <text x="220" y="165" font-family="sans-serif" font-size="16">r₂</text> <path d="M 50 135 L 53.0 115.6" stroke="red" stroke-width="2"></path> <path d="M 50 115 L 53.0 115.6" stroke="red" stroke-width="1"></path> <text x="55" y="135" font-family="sans-serif" font-size="16" fill="red">Δr</text> <line x1="50" y1="125" x2="400" y2="180" stroke="purple" stroke-width="1" stroke-dasharray="3,3"></line> <path d="M 80 125 A 30 30 0 0 1 78.4 133.8" stroke="purple" fill="none"></path> <text x="85" y="135" font-family="sans-serif" font-size="16" fill="purple">θ</text> <line x1="40" y1="115" x2="40" y2="135" stroke="black" stroke-width="1"></line> <text x="20" y="130" font-family="sans-serif" font-size="16">d</text></svg><p> На рисунке обозначены:<br> $S_1$ и $S_2$ — две узкие щели, которые по принципу Гюйгенса-Френеля становятся когерентными источниками вторичных волн.<br> $d$ — расстояние между центрами щелей.<br> $L$ — расстояние от экрана со щелями до наблюдательного экрана.<br> $P$ — произвольная точка на экране, в которой наблюдается результат интерференции.<br> $r_1$ и $r_2$ — расстояния (пути), проходимые волнами от щелей $S_1$ и $S_2$ до точки $P$ соответственно.<br> $\theta$ — угол, под которым видна точка $P$ из середины отрезка, соединяющего щели.</p><p>Ключевой величиной, определяющей результат интерференции в точке $P$, является <strong>разность хода волн</strong>. Это разница в расстояниях, которые проходят волны от источников $S_1$ и $S_2$ до точки $P$. Она обозначается как $\Delta r$ и равна:</p><p>$\Delta r = r_2 - r_1$</p><p>На рисунке разность хода $\Delta r$ схематически показана красным отрезком. В приближении, когда расстояние до экрана $L$ значительно больше расстояния между щелями $d$ ($L \gg d$), разность хода можно с хорошей точностью вычислить по геометрической формуле:</p><p>$\Delta r = d \sin\theta$</p><p>Результат интерференции зависит от того, как разность хода соотносится с длиной волны света $\lambda$:<br> <strong>Условие максимума (светлая полоса):</strong> волны приходят в точку $P$ в одной фазе и усиливают друг друга. Это происходит, когда разность хода равна целому числу длин волн.<br> $\Delta r = m \lambda$, где $m = 0, \pm1, \pm2, ...$<br><br> <strong>Условие минимума (темная полоса):</strong> волны приходят в точку $P$ в противофазе и гасят друг друга. Это происходит, когда разность хода равна полуцелому числу длин волн.<br> $\Delta r = (m + \frac{1}{2}) \lambda$, где $m = 0, \pm1, \pm2, ...$</p><p><strong>Ответ:</strong> Схема опыта Юнга с изображением хода волн и обозначением разности хода представлена на рисунке и в пояснениях выше. Разность хода волн — это разница расстояний $\Delta r = r_2 - r_1$, которая для данного эксперимента может быть найдена по формуле $\Delta r = d \sin\theta$.</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" => "1435354" "type" => "task" ] "previous" => array:2 [ "refs" => "1435352" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1118 #items: array:1 [ 0 => App\Models\Book {#1140} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1125 #items: array:1 [ 0 => App\Models\BookPage {#1088 #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" => 1435693 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-58" "field_display_title" => "58" "field_folder" => "3" "field_image_name" => "58" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1115 #items: array:1 [ 0 => App\Models\Branch {#1137} ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1111 #items: array:1 [ 0 => App\Models\Book {#1140} ] #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 {#1112 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1085 #items: array:1 [ 0 => App\Models\Element {#1087 #connection: "mysql" #table: "elements" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array:6 [ "id" => 1699080 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1046 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1699080 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1046 …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" => "1435694" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435692" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1326 #items: array:5 [ 0 => App\Models\Task {#1338 #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" => 1435350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "57" "field_page_end" => "58" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-1" "field_display_title" => "1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1339 …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 {#1340 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1341 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1342 …2} "content" => Illuminate\Database\Eloquent\Collection {#1353 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1358 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435350 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "57" "field_page_end" => "58" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-1" "field_display_title" => "1" "field_outside_task" => "0" "field_task_type" => Illuminate\Database\Eloquent\Collection {#1339 …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 {#1340 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1341 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1342 …2} "content" => Illuminate\Database\Eloquent\Collection {#1353 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1358 …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 {#1343 #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" => 1435351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1345 …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 {#1344 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1350 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1349 …2} "content" => Illuminate\Database\Eloquent\Collection {#1346 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1354 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435351 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1345 …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 {#1344 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1350 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1349 …2} "content" => Illuminate\Database\Eloquent\Collection {#1346 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1354 …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 {#1347 #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" => 1435352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1348 …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 {#1355 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1360 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1352 …2} "content" => Illuminate\Database\Eloquent\Collection {#1351 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1374 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435352 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1348 …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 {#1355 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1360 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1352 …2} "content" => Illuminate\Database\Eloquent\Collection {#1351 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1374 …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 {#1369 #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" => 1435353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1356 …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 {#1376 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1372 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1370 …2} "content" => Illuminate\Database\Eloquent\Collection {#1373 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1371 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1356 …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 {#1376 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1372 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1370 …2} "content" => Illuminate\Database\Eloquent\Collection {#1373 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1371 …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 {#1381 #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" => 1435354 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-5" "field_display_title" => "5" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1382 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" => null "breadcrumbs" => [] …8 ] #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" => 1435693 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-58" "field_display_title" => "58" "field_folder" => "3" "field_image_name" => "58" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1115} "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1111} "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 {#1112} "content" => Illuminate\Database\Eloquent\Collection {#1085} "next" => array:2 [ "refs" => "1435694" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435692" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1326} ] #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" => 1435353 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "58" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/51-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1009} "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 {#1007} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1048} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1127} "content" => Illuminate\Database\Eloquent\Collection {#1084} "next" => array:2 [ "refs" => "1435354" "type" => "task" ] "previous" => array:2 [ "refs" => "1435352" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1118} "page" => array:2 [ "refs" => "1435693" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№4 (с. 58)
Условие. №4 (с. 58)
скриншот условия
4. Изобразите ход волн в опыте Юнга. Обозначьте на рисунке разность хода волн.
Решение. №4 (с. 58)
Решение:
Опыт Юнга — это классический эксперимент, демонстрирующий явление интерференции света и доказывающий его волновую природу. В этом опыте когерентный свет (например, от лазера) проходит через две близко расположенные щели и создает на удаленном экране интерференционную картину в виде чередующихся светлых и темных полос.
Схема опыта, иллюстрирующая ход волн и разность хода, представлена на рисунке ниже.
На рисунке обозначены:
$S_1$ и $S_2$ — две узкие щели, которые по принципу Гюйгенса-Френеля становятся когерентными источниками вторичных волн.
$d$ — расстояние между центрами щелей.
$L$ — расстояние от экрана со щелями до наблюдательного экрана.
$P$ — произвольная точка на экране, в которой наблюдается результат интерференции.
$r_1$ и $r_2$ — расстояния (пути), проходимые волнами от щелей $S_1$ и $S_2$ до точки $P$ соответственно.
$\theta$ — угол, под которым видна точка $P$ из середины отрезка, соединяющего щели.
Ключевой величиной, определяющей результат интерференции в точке $P$, является разность хода волн. Это разница в расстояниях, которые проходят волны от источников $S_1$ и $S_2$ до точки $P$. Она обозначается как $\Delta r$ и равна:
$\Delta r = r_2 - r_1$
На рисунке разность хода $\Delta r$ схематически показана красным отрезком. В приближении, когда расстояние до экрана $L$ значительно больше расстояния между щелями $d$ ($L \gg d$), разность хода можно с хорошей точностью вычислить по геометрической формуле:
$\Delta r = d \sin\theta$
Результат интерференции зависит от того, как разность хода соотносится с длиной волны света $\lambda$:
Условие максимума (светлая полоса): волны приходят в точку $P$ в одной фазе и усиливают друг друга. Это происходит, когда разность хода равна целому числу длин волн.
$\Delta r = m \lambda$, где $m = 0, \pm1, \pm2, ...$
Условие минимума (темная полоса): волны приходят в точку $P$ в противофазе и гасят друг друга. Это происходит, когда разность хода равна полуцелому числу длин волн.
$\Delta r = (m + \frac{1}{2}) \lambda$, где $m = 0, \pm1, \pm2, ...$
Ответ: Схема опыта Юнга с изображением хода волн и обозначением разности хода представлена на рисунке и в пояснениях выше. Разность хода волн — это разница расстояний $\Delta r = r_2 - r_1$, которая для данного эксперимента может быть найдена по формуле $\Delta r = d \sin\theta$.
Другие задания:
Помогло решение? Оставьте отзыв в комментариях ниже.
Присоединяйтесь к Телеграм-группе @top_gdz
ПрисоединитьсяМы подготовили для вас ответ c подробным объяснением домашего задания по физике за 9 класс, для упражнения номер 4 расположенного на странице 58 для 3-й части к рабочей тетради 2021 года издания для учащихся школ и гимназий.
Теперь на нашем сайте ГДЗ.ТОП вы всегда легко и бесплатно найдёте условие с правильным ответом на вопрос «Как решить ДЗ» и «Как сделать» задание по физике к упражнению №4 (с. 58), авторов: Грачев (Александр Васильевич), Погожев (Владимир Александрович), Боков (Павел Юрьевич), Вишнякова (Екатерина Анатольевна), 3-й части ФГОС (старый) учебного пособия издательства Просвещение.