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Номер 7, страница 21, 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 41. Законы отражения света - номер 7, страница 21.
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" => 1435221 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-7" "field_display_title" => "7" "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" => 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 {#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" => 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 {#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" => 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 {#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 {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …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" => "6" "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" => 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 {#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-rabochaya-tetrad" "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" => 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 {#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 {#1053 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1054 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1056 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1058 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1060 …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" => "6" "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" => 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 {#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-rabochaya-tetrad" "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" => 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 {#1039} "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 {#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 {#1187 #items: array:3 [ 0 => App\Models\Branch {#1197 #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 {#1201 #items: array:1 [ 0 => App\Models\Term {#1198 #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 {#1234 #items: array:1 [ 0 => App\Models\Book {#1200 #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 {#1202 #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: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 {#1203 #items: array:1 [ 0 => App\Models\Term {#1204 #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 {#1205 #items: array:1 [ 0 => App\Models\Term {#1206 #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 {#1207 #items: array:4 [ 0 => App\Models\Term {#1208 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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 {#1209 #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 {#1210 #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 {#1211 #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 {#1212 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1213 #items: array:1 [ 0 => App\Models\Term {#1214 #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 {#1215 #items: array:1 [ 0 => App\Models\Term {#1216 #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 {#1217 #items: array:1 [ 0 => App\Models\Term {#1218 #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 {#1219 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1220 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1221 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1222 #items: array:1 [ 0 => App\Models\Term {#1223 #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 {#1224 #items: array:1 [ 0 => App\Models\Term {#1225 #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 {#1226 #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 {#1227 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1228 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1229 #items: [] #escapeWhenCastingToString: false } "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1230 #items: array:1 [ 0 => App\Models\Term {#1231 #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 {#1202} "field_class" => Illuminate\Database\Eloquent\Collection {#1203} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1205} "field_author" => Illuminate\Database\Eloquent\Collection {#1207} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1212} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1213} "field_country" => Illuminate\Database\Eloquent\Collection {#1215} "field_city" => Illuminate\Database\Eloquent\Collection {#1217} "field_series" => Illuminate\Database\Eloquent\Collection {#1219} "field_umk" => Illuminate\Database\Eloquent\Collection {#1220} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1221} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1222} "field_publication_number" => "6" "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1224} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1226} "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 {#1227} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1228} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1229} "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1230} "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 {#1232 #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 {#1201} "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 {#1234} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1232} ] #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 {#1233 #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 {#1238 #items: array:1 [ 0 => App\Models\Term {#1235 #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 {#1237 #items: array:1 [ 0 => App\Models\Book {#1200} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1236 #items: array:1 [ 0 => App\Models\Branch {#1034} ] #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 {#1238} "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 {#1237} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1236} ] #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 {#1239 #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" => 1434855 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Законы отражения света" "field_branch_order" => "41" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1243 #items: array:1 [ 0 => App\Models\Term {#1240 #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" => "20" "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 {#1242 #items: array:1 [ 0 => App\Models\Book {#1200} ] #escapeWhenCastingToString: false } "branch_parent" => Illuminate\Database\Eloquent\Collection {#1319 #items: array:1 [ 0 => App\Models\Branch {#1241 #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 {#1245 …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 {#1246 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1279 …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 {#1245 …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 {#1246 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1279 …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" => 1434855 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Законы отражения света" "field_branch_order" => "41" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1243} "field_page_start" => "20" "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 {#1242} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1319} ] #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 {#1181 #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" => 1698609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172 #items: array:1 [ 0 => App\Models\Edition {#1180 #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 {#1177 …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 {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1176 …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 {#1177 …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 {#1178 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1175 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1176 …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" => "1435221" "type" => "task" ] "text" => "<p><strong>7.</strong> Угол между падающим на плоское зеркало лучом света и плоскостью зеркала равен $\alpha = 30^{\circ}$. Определите углы падения и отражения. Сделайте поясняющий рисунок.</p><p><strong><em>Решение.</em></strong></p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "2010" "height" => 309 "path" => "/media/fizika_09/grachev-rt/0-41/7-1.webp?ts=1759402825" ] ] ] #original: array:7 [ "id" => 1698609 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1172} "task" => array:2 [ "refs" => "1435221" "type" => "task" ] "text" => "<p><strong>7.</strong> Угол между падающим на плоское зеркало лучом света и плоскостью зеркала равен $\alpha = 30^{\circ}$. Определите углы падения и отражения. Сделайте поясняющий рисунок.</p><p><strong><em>Решение.</em></strong></p>" "img" => array:1 [ 0 => array:5 [ "name" => "7-1.jpg" "alt" => null "width" => "2010" "height" => 309 "path" => "/media/fizika_09/grachev-rt/0-41/7-1.webp?ts=1759402825" ] ] ] #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 {#1174 #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" => 1734595 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160 #items: array:1 [ 0 => App\Models\Edition {#1173 #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 {#1171 …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 {#1168 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166 …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 {#1171 …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 {#1168 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1169 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1166 …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" => "1435221" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Угол между падающим лучом и плоскостью зеркала: $\alpha = 30^{\circ}$</p> <p><strong>Найти:</strong></p> <p>Угол падения $\beta$ - ?</p> <p>Угол отражения $\gamma$ - ?</p> <p><strong>Решение:</strong></p> <p>Угол падения, обозначаемый $\beta$, — это угол между падающим лучом света и перпендикуляром (нормалью), проведённым к поверхности зеркала в точке падения луча. Угол отражения, обозначаемый $\gamma$, — это угол между отражённым лучом и этой же нормалью.</p> <p>В условии задачи дан угол $\alpha$, который является углом между падающим лучом и самой плоскостью зеркала.</p> <p>Нормаль по определению перпендикулярна поверхности, поэтому угол между нормалью и плоскостью зеркала составляет $90^{\circ}$.</p> <p>Из поясняющего рисунка видно, что угол падения $\beta$ и угол $\alpha$ вместе образуют прямой угол. Математически это можно записать так:</p> <p>$\beta + \alpha = 90^{\circ}$</p> <p>Используя это соотношение, мы можем найти угол падения:</p> <p>$\beta = 90^{\circ} - \alpha$</p> <p>Подставим известное значение $\alpha$:</p> <p>$\beta = 90^{\circ} - 30^{\circ} = 60^{\circ}$</p> <p>Согласно закону отражения света, угол отражения всегда равен углу падения:</p> <p>$\gamma = \beta$</p> <p>Следовательно, угол отражения также равен $60^{\circ}$:</p> <p>$\gamma = 60^{\circ}$</p> <p><strong>Поясняющий рисунок:</strong></p> <img src="data:image/svg+xml;base64,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" alt="Рисунок, поясняющий отражение света от плоского зеркала" width="400" height="250" loading="lazy"> <p><strong>Ответ:</strong> угол падения $\beta = 60^{\circ}$, угол отражения $\gamma = 60^{\circ}$.</p>" ] #original: array:6 [ "id" => 1734595 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1160} "task" => array:2 [ "refs" => "1435221" "type" => "task" ] "text" => "<p><strong>Дано:</strong></p> <p>Угол между падающим лучом и плоскостью зеркала: $\alpha = 30^{\circ}$</p> <p><strong>Найти:</strong></p> <p>Угол падения $\beta$ - ?</p> <p>Угол отражения $\gamma$ - ?</p> <p><strong>Решение:</strong></p> <p>Угол падения, обозначаемый $\beta$, — это угол между падающим лучом света и перпендикуляром (нормалью), проведённым к поверхности зеркала в точке падения луча. Угол отражения, обозначаемый $\gamma$, — это угол между отражённым лучом и этой же нормалью.</p> <p>В условии задачи дан угол $\alpha$, который является углом между падающим лучом и самой плоскостью зеркала.</p> <p>Нормаль по определению перпендикулярна поверхности, поэтому угол между нормалью и плоскостью зеркала составляет $90^{\circ}$.</p> <p>Из поясняющего рисунка видно, что угол падения $\beta$ и угол $\alpha$ вместе образуют прямой угол. Математически это можно записать так:</p> <p>$\beta + \alpha = 90^{\circ}$</p> <p>Используя это соотношение, мы можем найти угол падения:</p> <p>$\beta = 90^{\circ} - \alpha$</p> <p>Подставим известное значение $\alpha$:</p> <p>$\beta = 90^{\circ} - 30^{\circ} = 60^{\circ}$</p> <p>Согласно закону отражения света, угол отражения всегда равен углу падения:</p> <p>$\gamma = \beta$</p> <p>Следовательно, угол отражения также равен $60^{\circ}$:</p> <p>$\gamma = 60^{\circ}$</p> <p><strong>Поясняющий рисунок:</strong></p> <img src="data:image/svg+xml;base64,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" alt="Рисунок, поясняющий отражение света от плоского зеркала" width="400" height="250" loading="lazy"> <p><strong>Ответ:</strong> угол падения $\beta = 60^{\circ}$, угол отражения $\gamma = 60^{\circ}$.</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" => "1435222" "type" => "task" ] "previous" => array:2 [ "refs" => "1435220" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1183 #items: array:1 [ 0 => App\Models\Book {#1200} ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1185 #items: array:1 [ 0 => App\Models\BookPage {#1153 #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" => 1435656 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/page-3-21" "field_display_title" => "21" "field_folder" => "3" "field_image_name" => "21" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1167 #items: array:1 [ 0 => App\Models\Branch {#1197} ] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1165 #items: array:1 [ 0 => App\Models\Book {#1200} ] #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 {#1164 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1150 #items: array:1 [ 0 => App\Models\Element {#1155 #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" => 1699043 "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" => 1699043 "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" => "1435657" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1435655" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1415 #items: array:6 [ 0 => App\Models\Task {#1427 #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" => 1435216 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1428 …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 {#1429 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1430 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1431 …2} "content" => Illuminate\Database\Eloquent\Collection {#1433 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1439 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435216 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-2" "field_display_title" => "2" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1428 …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 {#1429 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1430 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1431 …2} "content" => Illuminate\Database\Eloquent\Collection {#1433 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1439 …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 {#1434 #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" => 1435217 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1432 …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 {#1441 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1437 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1435 …2} "content" => Illuminate\Database\Eloquent\Collection {#1436 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1451 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435217 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-3" "field_display_title" => "3" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1432 …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 {#1441 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1437 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1435 …2} "content" => Illuminate\Database\Eloquent\Collection {#1436 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1451 …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 {#1446 #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" => 1435218 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1438 …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 {#1453 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1449 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1447 …2} "content" => Illuminate\Database\Eloquent\Collection {#1448 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1463 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1435218 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "21" "field_page_end" => null "field_url" => "/9-klass/fizika/grachev-rabochaya-tetrad/41-4" "field_display_title" => "4" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1438 …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 {#1453 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1449 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1447 …2} "content" => Illuminate\Database\Eloquent\Collection {#1448 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1463 …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 {#1458 #connection: "mysql" #table: "tasks" #primaryKey: "id" #keyType: "int" +incrementing: true #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false 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"refs" => "1435220" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1183} "page" => array:2 [ "refs" => "1435656" "type" => "book_page" ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] }
№7 (с. 21)
Условие. №7 (с. 21)
скриншот условия
7. Угол между падающим на плоское зеркало лучом света и плоскостью зеркала равен $\alpha = 30^{\circ}$. Определите углы падения и отражения. Сделайте поясняющий рисунок.
Решение.
Решение. №7 (с. 21)
Дано:
Угол между падающим лучом и плоскостью зеркала: $\alpha = 30^{\circ}$
Найти:
Угол падения $\beta$ - ?
Угол отражения $\gamma$ - ?
Решение:
Угол падения, обозначаемый $\beta$, — это угол между падающим лучом света и перпендикуляром (нормалью), проведённым к поверхности зеркала в точке падения луча. Угол отражения, обозначаемый $\gamma$, — это угол между отражённым лучом и этой же нормалью.
В условии задачи дан угол $\alpha$, который является углом между падающим лучом и самой плоскостью зеркала.
Нормаль по определению перпендикулярна поверхности, поэтому угол между нормалью и плоскостью зеркала составляет $90^{\circ}$.
Из поясняющего рисунка видно, что угол падения $\beta$ и угол $\alpha$ вместе образуют прямой угол. Математически это можно записать так:
$\beta + \alpha = 90^{\circ}$
Используя это соотношение, мы можем найти угол падения:
$\beta = 90^{\circ} - \alpha$
Подставим известное значение $\alpha$:
$\beta = 90^{\circ} - 30^{\circ} = 60^{\circ}$
Согласно закону отражения света, угол отражения всегда равен углу падения:
$\gamma = \beta$
Следовательно, угол отражения также равен $60^{\circ}$:
$\gamma = 60^{\circ}$
Поясняющий рисунок:
Ответ: угол падения $\beta = 60^{\circ}$, угол отражения $\gamma = 60^{\circ}$.
Другие задания:
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