gdz.top
Номер 12, страница 9 - гдз по физике 8 класс учебник Изергин
Авторы: Изергин Э. Т.
Тип: Учебник
Издательство: Русское слово
Год издания: 2019 - 2026
Цвет обложки: синий
ISBN: 978-5-533-01067-2
Популярные ГДЗ в 8 классе
Глава I. Тепловые явления. Параграф 1. Внутренняя энергия - номер 12, страница 9.
App\Models\Task {#1024 // 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" => 1492219 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-12" "field_display_title" => "12" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#331 #items: array:1 [ 0 => App\Models\Term {#1029 #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 {#1026 #items: [] #escapeWhenCastingToString: false } "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#342 #items: array:1 [ 0 => App\Models\Branch {#1023 #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" => 1492157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333 #items: array:1 [ 0 => App\Models\Term {#1033 #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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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 [ "field_accusative_case" => "Главу" "field_creative_case" => "Главой" "field_dative_case" => "Главе" "field_genitive_case" => "Главы" "field_nominative_case" => "Глава" "field_prepositional_case" => "Главе" ] "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" => "4" "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 {#1030 #items: array:1 [ 0 => App\Models\Book {#1032 #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" => 4168 "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 {#1034 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_class" => Illuminate\Database\Eloquent\Collection {#1036 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author" => Illuminate\Database\Eloquent\Collection {#1040 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042 #items: [] #escapeWhenCastingToString: false } "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_country" => Illuminate\Database\Eloquent\Collection {#1045 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_city" => Illuminate\Database\Eloquent\Collection {#1047 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_series" => Illuminate\Database\Eloquent\Collection {#1049 #items: [] #escapeWhenCastingToString: false } "field_umk" => Illuminate\Database\Eloquent\Collection {#1050 #items: [] #escapeWhenCastingToString: false } "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051 #items: [] #escapeWhenCastingToString: false } "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055 #items: [] #escapeWhenCastingToString: false } "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ …4] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056 #items: [] #escapeWhenCastingToString: false } "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057 #items: [] #escapeWhenCastingToString: false } "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058 #items: [] #escapeWhenCastingToString: false } "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059 #items: array:1 [ …1] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 …2 ] ] #original: array:50 [ "id" => 4168 "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 {#1034} "field_class" => Illuminate\Database\Eloquent\Collection {#1036} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1038} "field_author" => Illuminate\Database\Eloquent\Collection {#1040} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1042} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1043} "field_country" => Illuminate\Database\Eloquent\Collection {#1045} "field_city" => Illuminate\Database\Eloquent\Collection {#1047} "field_series" => Illuminate\Database\Eloquent\Collection {#1049} "field_umk" => Illuminate\Database\Eloquent\Collection {#1050} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1051} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1052} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1054} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1055} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1056} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1057} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1058} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1059} "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 {#1061 #items: [] #escapeWhenCastingToString: false } ] #original: array:24 [ "id" => 1492157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#333} "field_page_start" => "4" "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 {#1030} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1061} ] #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 {#1062 #items: array:2 [ 0 => App\Models\Branch {#1023} 1 => App\Models\Branch {#1063 #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" => 1492158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Внутренняя энергия" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1064 #items: array:1 [ 0 => App\Models\Term {#1065 #connection: "mysql" #table: "terms" #primaryKey: "id" #keyType: "int" +incrementing: false #with: [] #withCount: [] +preventsLazyLoading: false #perPage: 15 +exists: true +wasRecentlyCreated: false #escapeWhenCastingToString: false #attributes: array: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" => "4" "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 {#1066 #items: array:1 [ 0 => App\Models\Book {#1067 #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" => 4168 "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 {#1068 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1093 …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" => 4168 "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 {#1068 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1070 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1072 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1074 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1076 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1077 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1079 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1081 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1083 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1084 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1085 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1086 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1088 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1089 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1090 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1091 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1092 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1093 …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 {#1095 #items: array:1 [ 0 => App\Models\Branch {#1096 #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" => 1492157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_page_start" => "4" "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 {#1099 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 …2} ] #original: array:24 [ "id" => 1492157 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Тепловые явления" "field_branch_order" => "I" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1097 …2} "field_page_start" => "4" "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 {#1099 …2} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1128 …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" => 1492158 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_display_title" => "Внутренняя энергия" "field_branch_order" => "1" "field_url" => null "field_branch_type" => Illuminate\Database\Eloquent\Collection {#1064} "field_page_start" => "4" "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 {#1066} "branch_parent" => Illuminate\Database\Eloquent\Collection {#1095} ] #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 {#1129 #items: array:2 [ 0 => App\Models\Element {#1130 #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" => 1774388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131 #items: array:1 [ 0 => App\Models\Edition {#1132 #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" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …2} "field_content_source" => null ] #original: array:21 [ "id" => 6496 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Условие" "field_order" => "1" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1133 …2} "field_content_type" => "free" "field_content_mode" => "text, image" "field_page_content_mode" => "image" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Автор" "field_moderator" => "stas" "field_edition_type" => "statement" "field_root_dir" => "0-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1135 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1136 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1137 …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" => "1492219" "type" => "task" ] "text" => "<p><strong>12*.</strong> Выполните экспериментальное задание 1 на с. 249.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1276" "height" => 152 "path" => "/media/fizika_08/izergin-u/0-01/12-1.webp?ts=1761329146" ] ] ] #original: array:7 [ "id" => 1774388 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1131} "task" => array:2 [ "refs" => "1492219" "type" => "task" ] "text" => "<p><strong>12*.</strong> Выполните экспериментальное задание 1 на с. 249.</p>" "img" => array:1 [ 0 => array:5 [ "name" => "12-1.jpg" "alt" => null "width" => "1276" "height" => 152 "path" => "/media/fizika_08/izergin-u/0-01/12-1.webp?ts=1761329146" ] ] ] #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 {#1138 #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" => 1851560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139 #items: array:1 [ 0 => App\Models\Edition {#1140 #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" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …2} "field_content_source" => null ] #original: array:21 [ "id" => 7014 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "title" => "Решение" "field_order" => "2" "field_publisher" => Illuminate\Database\Eloquent\Collection {#1141 …2} "field_content_type" => "free" "field_content_mode" => "text" "field_page_content_mode" => "" "field_content_text_checked" => "0" "field_page_content_text_checked" => "0" "field_solution_author" => "Gemini 2.5 Pro" "field_moderator" => "tolik" "field_edition_type" => "solution" "field_root_dir" => "1-" "field_responsible" => Illuminate\Database\Eloquent\Collection {#1143 …2} "field_comment" => null "field_similar_book" => Illuminate\Database\Eloquent\Collection {#1144 …2} "field_process_formula" => "katex" "field_edition_group" => Illuminate\Database\Eloquent\Collection {#1145 …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" => "1492219" "type" => "task" ] "text" => "<p><strong>Экспериментальное задание 1: Определение фокусного расстояния собирающей линзы</strong></p><p><strong>Цель работы:</strong> Экспериментально определить фокусное расстояние собирающей линзы.</p><p><strong>Оборудование:</strong> собирающая линза, экран, источник света (предмет), линейка или оптическая скамья.</p><p><strong>Краткое теоретическое обоснование и описание эксперимента:</strong></p><p>Для определения фокусного расстояния собирающей линзы используется формула тонкой линзы, которая связывает расстояние от предмета до линзы $\text{d}$, расстояние от линзы до изображения $f'$ и фокусное расстояние линзы $\text{F}$:</p><p>$ \frac{1}{F} = \frac{1}{d} + \frac{1}{f'} $</p><p>В ходе эксперимента на оптической скамье размещают источник света (предмет), собирающую линзу и экран. Устанавливая предмет на различных расстояниях $\text{d}$ от линзы, получают его чёткое действительное изображение на экране. Для каждого положения измеряют расстояние $\text{d}$ и соответствующее ему расстояние $f'$. Проводят серию из нескольких измерений для повышения точности результата. На основе полученных данных производятся вычисления.</p><p>Ниже представлен расчёт на основе гипотетических экспериментальных данных.</p><p><strong>Дано:</strong></p><p>Результаты трёх измерений расстояния от предмета до линзы ($\text{d}$) и от линзы до изображения ($f'$):</p><p>Опыт 1: $d_1 = 25,0$ см, $f'_1 = 37,8$ см</p><p>Опыт 2: $d_2 = 30,0$ см, $f'_2 = 30,2$ см</p><p>Опыт 3: $d_3 = 40,0$ см, $f'_3 = 23,8$ см</p><p>Перевод в систему СИ:</p><p>$d_1 = 0,250$ м, $f'_1 = 0,378$ м</p><p>$d_2 = 0,300$ м, $f'_2 = 0,302$ м</p><p>$d_3 = 0,400$ м, $f'_3 = 0,238$ м</p><p>Приборная погрешность измерения расстояний (цена деления линейки 1 мм) $\Delta d_{приб} = \Delta f'_{приб} = 0,1$ см $= 0,001$ м.</p><p><strong>Найти:</strong></p><p>Фокусное расстояние линзы $\text{F}$ и его погрешность $\Delta F$.</p><p><strong>Решение:</strong></p><p>Для определения фокусного расстояния собирающей линзы воспользуемся формулой тонкой линзы, выразив из неё $\text{F}$:</p><p>$ F = \frac{d \cdot f'}{d + f'} $</p><p><strong>1.</strong> Вычисление фокусного расстояния для каждого опыта:</p><p><strong>Опыт 1:</strong></p><p>$ F_1 = \frac{d_1 \cdot f'_1}{d_1 + f'_1} = \frac{0,250 \cdot 0,378}{0,250 + 0,378} = \frac{0,0945}{0,628} \approx 0,1505 $ м</p><p><strong>Опыт 2:</strong></p><p>$ F_2 = \frac{d_2 \cdot f'_2}{d_2 + f'_2} = \frac{0,300 \cdot 0,302}{0,300 + 0,302} = \frac{0,0906}{0,602} \approx 0,1505 $ м</p><p><strong>Опыт 3:</strong></p><p>$ F_3 = \frac{d_3 \cdot f'_3}{d_3 + f'_3} = \frac{0,400 \cdot 0,238}{0,400 + 0,238} = \frac{0,0952}{0,638} \approx 0,1492 $ м</p><p><strong>2.</strong> Вычисление среднего значения фокусного расстояния:</p><p>$ F_{ср} = \frac{F_1 + F_2 + F_3}{3} = \frac{0,1505 + 0,1505 + 0,1492}{3} = \frac{0,4502}{3} \approx 0,1501 $ м</p><p><strong>3.</strong> Расчёт абсолютной погрешности измерений:</p><p>Найдём абсолютные отклонения для каждого измерения (случайная погрешность):</p><p>$ \Delta F_1 = |F_{ср} - F_1| = |0,1501 - 0,1505| = 0,0004 $ м</p><p>$ \Delta F_2 = |F_{ср} - F_2| = |0,1501 - 0,1505| = 0,0004 $ м</p><p>$ \Delta F_3 = |F_{ср} - F_3| = |0,1501 - 0,1492| = 0,0009 $ м</p><p>Средняя абсолютная случайная погрешность:</p><p>$ \Delta F_{случ} = \frac{\Delta F_1 + \Delta F_2 + \Delta F_3}{3} = \frac{0,0004 + 0,0004 + 0,0009}{3} \approx 0,0006 $ м</p><p>Оценим приборную погрешность для второго опыта (как наиболее близкого к случаю $d=f'=2F$, где погрешность минимальна):</p><p>$ \Delta F_{приб} = F_{ср}^2 \left( \frac{\Delta d_{приб}}{d_2^2} + \frac{\Delta f'_{приб}}{(f'_2)^2} \right) \approx (0,1501)^2 \left( \frac{0,001}{(0,300)^2} + \frac{0,001}{(0,302)^2} \right) \approx 0,0225 \left( 0,0111 + 0,0110 \right) \approx 0,0005 $ м</p><p>Полная абсолютная погрешность равна сумме случайной и приборной погрешностей:</p><p>$ \Delta F = \Delta F_{случ} + \Delta F_{приб} \approx 0,0006 + 0,0005 = 0,0011 $ м</p><p>Округлим погрешность до одной значащей цифры: $ \Delta F \approx 0,001 $ м. Тогда результат для среднего значения фокусного расстояния округляем до того же десятичного знака:</p><p>$ F_{ср} = 0,150 $ м</p><p>Окончательный результат запишем в виде $ F = F_{ср} \pm \Delta F $:</p><p>$ F = (0,150 \pm 0,001) $ м, или $ F = (15,0 \pm 0,1) $ см.</p><p><strong>4.</strong> Расчёт относительной погрешности:</p><p>$ \varepsilon = \frac{\Delta F}{F_{ср}} \cdot 100\% = \frac{0,001}{0,150} \cdot 100\% \approx 0,7\% $</p><p>Так как относительная погрешность мала, результат можно считать достоверным.</p><p><strong>Ответ:</strong> Фокусное расстояние линзы, определённое экспериментально, составляет $ F = (15,0 \pm 0,1) $ см. Относительная погрешность измерений составила примерно $0,7\%$.</p>" ] #original: array:6 [ "id" => 1851560 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1139} "task" => array:2 [ "refs" => "1492219" "type" => "task" ] "text" => "<p><strong>Экспериментальное задание 1: Определение фокусного расстояния собирающей линзы</strong></p><p><strong>Цель работы:</strong> Экспериментально определить фокусное расстояние собирающей линзы.</p><p><strong>Оборудование:</strong> собирающая линза, экран, источник света (предмет), линейка или оптическая скамья.</p><p><strong>Краткое теоретическое обоснование и описание эксперимента:</strong></p><p>Для определения фокусного расстояния собирающей линзы используется формула тонкой линзы, которая связывает расстояние от предмета до линзы $\text{d}$, расстояние от линзы до изображения $f'$ и фокусное расстояние линзы $\text{F}$:</p><p>$ \frac{1}{F} = \frac{1}{d} + \frac{1}{f'} $</p><p>В ходе эксперимента на оптической скамье размещают источник света (предмет), собирающую линзу и экран. Устанавливая предмет на различных расстояниях $\text{d}$ от линзы, получают его чёткое действительное изображение на экране. Для каждого положения измеряют расстояние $\text{d}$ и соответствующее ему расстояние $f'$. Проводят серию из нескольких измерений для повышения точности результата. На основе полученных данных производятся вычисления.</p><p>Ниже представлен расчёт на основе гипотетических экспериментальных данных.</p><p><strong>Дано:</strong></p><p>Результаты трёх измерений расстояния от предмета до линзы ($\text{d}$) и от линзы до изображения ($f'$):</p><p>Опыт 1: $d_1 = 25,0$ см, $f'_1 = 37,8$ см</p><p>Опыт 2: $d_2 = 30,0$ см, $f'_2 = 30,2$ см</p><p>Опыт 3: $d_3 = 40,0$ см, $f'_3 = 23,8$ см</p><p>Перевод в систему СИ:</p><p>$d_1 = 0,250$ м, $f'_1 = 0,378$ м</p><p>$d_2 = 0,300$ м, $f'_2 = 0,302$ м</p><p>$d_3 = 0,400$ м, $f'_3 = 0,238$ м</p><p>Приборная погрешность измерения расстояний (цена деления линейки 1 мм) $\Delta d_{приб} = \Delta f'_{приб} = 0,1$ см $= 0,001$ м.</p><p><strong>Найти:</strong></p><p>Фокусное расстояние линзы $\text{F}$ и его погрешность $\Delta F$.</p><p><strong>Решение:</strong></p><p>Для определения фокусного расстояния собирающей линзы воспользуемся формулой тонкой линзы, выразив из неё $\text{F}$:</p><p>$ F = \frac{d \cdot f'}{d + f'} $</p><p><strong>1.</strong> Вычисление фокусного расстояния для каждого опыта:</p><p><strong>Опыт 1:</strong></p><p>$ F_1 = \frac{d_1 \cdot f'_1}{d_1 + f'_1} = \frac{0,250 \cdot 0,378}{0,250 + 0,378} = \frac{0,0945}{0,628} \approx 0,1505 $ м</p><p><strong>Опыт 2:</strong></p><p>$ F_2 = \frac{d_2 \cdot f'_2}{d_2 + f'_2} = \frac{0,300 \cdot 0,302}{0,300 + 0,302} = \frac{0,0906}{0,602} \approx 0,1505 $ м</p><p><strong>Опыт 3:</strong></p><p>$ F_3 = \frac{d_3 \cdot f'_3}{d_3 + f'_3} = \frac{0,400 \cdot 0,238}{0,400 + 0,238} = \frac{0,0952}{0,638} \approx 0,1492 $ м</p><p><strong>2.</strong> Вычисление среднего значения фокусного расстояния:</p><p>$ F_{ср} = \frac{F_1 + F_2 + F_3}{3} = \frac{0,1505 + 0,1505 + 0,1492}{3} = \frac{0,4502}{3} \approx 0,1501 $ м</p><p><strong>3.</strong> Расчёт абсолютной погрешности измерений:</p><p>Найдём абсолютные отклонения для каждого измерения (случайная погрешность):</p><p>$ \Delta F_1 = |F_{ср} - F_1| = |0,1501 - 0,1505| = 0,0004 $ м</p><p>$ \Delta F_2 = |F_{ср} - F_2| = |0,1501 - 0,1505| = 0,0004 $ м</p><p>$ \Delta F_3 = |F_{ср} - F_3| = |0,1501 - 0,1492| = 0,0009 $ м</p><p>Средняя абсолютная случайная погрешность:</p><p>$ \Delta F_{случ} = \frac{\Delta F_1 + \Delta F_2 + \Delta F_3}{3} = \frac{0,0004 + 0,0004 + 0,0009}{3} \approx 0,0006 $ м</p><p>Оценим приборную погрешность для второго опыта (как наиболее близкого к случаю $d=f'=2F$, где погрешность минимальна):</p><p>$ \Delta F_{приб} = F_{ср}^2 \left( \frac{\Delta d_{приб}}{d_2^2} + \frac{\Delta f'_{приб}}{(f'_2)^2} \right) \approx (0,1501)^2 \left( \frac{0,001}{(0,300)^2} + \frac{0,001}{(0,302)^2} \right) \approx 0,0225 \left( 0,0111 + 0,0110 \right) \approx 0,0005 $ м</p><p>Полная абсолютная погрешность равна сумме случайной и приборной погрешностей:</p><p>$ \Delta F = \Delta F_{случ} + \Delta F_{приб} \approx 0,0006 + 0,0005 = 0,0011 $ м</p><p>Округлим погрешность до одной значащей цифры: $ \Delta F \approx 0,001 $ м. Тогда результат для среднего значения фокусного расстояния округляем до того же десятичного знака:</p><p>$ F_{ср} = 0,150 $ м</p><p>Окончательный результат запишем в виде $ F = F_{ср} \pm \Delta F $:</p><p>$ F = (0,150 \pm 0,001) $ м, или $ F = (15,0 \pm 0,1) $ см.</p><p><strong>4.</strong> Расчёт относительной погрешности:</p><p>$ \varepsilon = \frac{\Delta F}{F_{ср}} \cdot 100\% = \frac{0,001}{0,150} \cdot 100\% \approx 0,7\% $</p><p>Так как относительная погрешность мала, результат можно считать достоверным.</p><p><strong>Ответ:</strong> Фокусное расстояние линзы, определённое экспериментально, составляет $ F = (15,0 \pm 0,1) $ см. Относительная погрешность измерений составила примерно $0,7\%$.</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" => "1492220" "type" => "task" ] "previous" => array:2 [ "refs" => "1492218" "type" => "task" ] "book" => Illuminate\Database\Eloquent\Collection {#1146 #items: array:1 [ 0 => App\Models\Book {#1147 #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" => 4168 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_tree_default_status" => "tasks" "field_pages_status" 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"siniy" ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #original: array:50 [ "id" => 4168 "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 {#1148} "field_class" => Illuminate\Database\Eloquent\Collection {#1150} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1152} "field_author" => Illuminate\Database\Eloquent\Collection {#1154} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1156} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1157} "field_country" => Illuminate\Database\Eloquent\Collection {#1159} "field_city" => Illuminate\Database\Eloquent\Collection {#1161} "field_series" => Illuminate\Database\Eloquent\Collection {#1163} "field_umk" => Illuminate\Database\Eloquent\Collection {#1164} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1165} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1166} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1168} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1169} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ 0 => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" ] "field_cover_alts" => array:1 [ 0 => "" ] "field_covers" => array:1 [ 0 => array:4 [ "path" => "/media/fizika_08/izergin-u/covers/cover1.webp?ts=1760998278" "alt" => "" "width" => "1608" "height" => "2576" ] ] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1170} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1171} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1172} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1173} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "breadcrumbs" => array:3 [ "class" => 379 "subject" => 556 "class_subject" => 492 ] ] #changes: [] #casts: [] #classCastCache: [] #attributeCastCache: [] #dateFormat: null #appends: [] #dispatchesEvents: [] #observables: [] #relations: [] #touches: [] +timestamps: true +usesUniqueIds: false #hidden: [] #visible: [] #fillable: [] #guarded: array:1 [ 0 => "*" ] } ] #escapeWhenCastingToString: false } "page" => Illuminate\Database\Eloquent\Collection {#1512 #items: array:1 [ 0 => App\Models\BookPage {#1179 #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" => 1491901 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_url" => "/8-klass/fizika/izergin-uchebnik/page-9" "field_display_title" => "9" "field_folder" => "1" "field_image_name" => "9" "field_branch_parent" => Illuminate\Database\Eloquent\Collection {#1182 #items: [] #escapeWhenCastingToString: false } "field_weight" => "0" "field_book_parent" => Illuminate\Database\Eloquent\Collection {#1181 #items: array:1 [ 0 => App\Models\Book {#1183 #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" => 4168 "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 {#1184 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1209 …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" => 4168 "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 {#1184 …2} "field_class" => Illuminate\Database\Eloquent\Collection {#1186 …2} "field_publisher" => Illuminate\Database\Eloquent\Collection {#1188 …2} "field_author" => Illuminate\Database\Eloquent\Collection {#1190 …2} "field_author_foreign" => Illuminate\Database\Eloquent\Collection {#1192 …2} "field_book_type" => Illuminate\Database\Eloquent\Collection {#1193 …2} "field_country" => Illuminate\Database\Eloquent\Collection {#1195 …2} "field_city" => Illuminate\Database\Eloquent\Collection {#1197 …2} "field_series" => Illuminate\Database\Eloquent\Collection {#1199 …2} "field_umk" => Illuminate\Database\Eloquent\Collection {#1200 …2} "field_level_of_education" => Illuminate\Database\Eloquent\Collection {#1201 …2} "field_standart_of_education" => Illuminate\Database\Eloquent\Collection {#1202 …2} "field_publication_number" => null "field_publication_type" => Illuminate\Database\Eloquent\Collection {#1204 …2} "field_under_the_edition" => Illuminate\Database\Eloquent\Collection {#1205 …2} "field_under_the_edition_degree" => null "field_cover_description" => null "field_publication_year" => "2019" "field_publication_year_until" => null "field_part" => "" "field_part_writing" => "" "field_second_foreign_language" => null "field_for_whom" => "Учебник для 8 класса общеобразовательных организаций" "field_allowed" => null "field_reserve_field" => null "field_link_to_source" => null "field_tasks_count" => "417" "field_priority" => null "field_default_folder" => "/fizika_08/izergin-u/" "field_isbn" => "978-5-533-01067-2" "field_cover" => array:1 [ …1] "field_cover_alts" => array:1 [ …1] "field_covers" => array:1 [ …1] "field_popular_book" => "0" "field_recommended_books" => Illuminate\Database\Eloquent\Collection {#1206 …2} "field_new_book" => Illuminate\Database\Eloquent\Collection {#1207 …2} "field_old_book" => Illuminate\Database\Eloquent\Collection {#1208 …2} "field_url" => "/8-klass/fizika/izergin-uchebnik" "field_cover_color" => Illuminate\Database\Eloquent\Collection {#1209 …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 } "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 {#1211 #items: [] #escapeWhenCastingToString: false } "content" => Illuminate\Database\Eloquent\Collection {#1212 #items: array:1 [ 0 => App\Models\Element {#1213 #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" => 1774802 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …2} "book_page" => array:2 [ …2] "img" => array:1 [ …1] ] #original: array:6 [ "id" => 1774802 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "edition" => Illuminate\Database\Eloquent\Collection {#1214 …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" => "1491902" "type" => "book_page" ] "previous" => array:2 [ "refs" => "1491900" "type" => "book_page" ] "tasks" => Illuminate\Database\Eloquent\Collection {#1221 #items: array:7 [ 0 => App\Models\Task {#1222 #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" => 1492213 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1223 …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 {#1225 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260 …2} "content" => Illuminate\Database\Eloquent\Collection {#1360 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1377 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492213 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-6" "field_display_title" => "6" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1223 …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 {#1225 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1226 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1260 …2} "content" => Illuminate\Database\Eloquent\Collection {#1360 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1377 …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 {#1378 #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" => 1492214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …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 {#1380 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1382 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1400 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492214 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-7" "field_display_title" => "7" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1379 …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 {#1380 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1381 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1382 …2} "content" => Illuminate\Database\Eloquent\Collection {#1383 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1400 …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 {#1401 #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" => 1492215 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1402 …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 {#1403 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1404 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1405 …2} "content" => Illuminate\Database\Eloquent\Collection {#1406 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1423 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492215 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-8" "field_display_title" => "8" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1402 …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 {#1403 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1404 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1405 …2} "content" => Illuminate\Database\Eloquent\Collection {#1406 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1423 …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 {#1424 #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" => 1492216 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1425 …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 {#1426 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1427 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1428 …2} "content" => Illuminate\Database\Eloquent\Collection {#1429 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1446 …2} "page" => array:2 [ …2] ] #original: array:24 [ "id" => 1492216 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-9" "field_display_title" => "9" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1425 …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 {#1426 …2} "top_parent_branch" => Illuminate\Database\Eloquent\Collection {#1427 …2} "parent_branches" => Illuminate\Database\Eloquent\Collection {#1428 …2} "content" => Illuminate\Database\Eloquent\Collection {#1429 …2} "next" => array:2 [ …2] "previous" => array:2 [ …2] "book" => Illuminate\Database\Eloquent\Collection {#1446 …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 {#1447 #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" => 1492217 "created_at" => "2026-04-10 13:58:26" "updated_at" => null "field_page_start" => "9" "field_page_end" => null "field_url" => "/8-klass/fizika/izergin-uchebnik/01-10" "field_display_title" => "10" "field_outside_task" => null "field_task_type" => Illuminate\Database\Eloquent\Collection {#1448 …2} "field_metatags_title" => null "field_metatags_description" => null "field_h1" => null "field_description_top" => null "field_description_bottom" => null "field_match" 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№12 (с. 9)
Условие. №12 (с. 9)
скриншот условия
12*. Выполните экспериментальное задание 1 на с. 249.
Решение. №12 (с. 9)
Экспериментальное задание 1: Определение фокусного расстояния собирающей линзы
Цель работы: Экспериментально определить фокусное расстояние собирающей линзы.
Оборудование: собирающая линза, экран, источник света (предмет), линейка или оптическая скамья.
Краткое теоретическое обоснование и описание эксперимента:
Для определения фокусного расстояния собирающей линзы используется формула тонкой линзы, которая связывает расстояние от предмета до линзы $\text{d}$, расстояние от линзы до изображения $f'$ и фокусное расстояние линзы $\text{F}$:
$ \frac{1}{F} = \frac{1}{d} + \frac{1}{f'} $
В ходе эксперимента на оптической скамье размещают источник света (предмет), собирающую линзу и экран. Устанавливая предмет на различных расстояниях $\text{d}$ от линзы, получают его чёткое действительное изображение на экране. Для каждого положения измеряют расстояние $\text{d}$ и соответствующее ему расстояние $f'$. Проводят серию из нескольких измерений для повышения точности результата. На основе полученных данных производятся вычисления.
Ниже представлен расчёт на основе гипотетических экспериментальных данных.
Дано:
Результаты трёх измерений расстояния от предмета до линзы ($\text{d}$) и от линзы до изображения ($f'$):
Опыт 1: $d_1 = 25,0$ см, $f'_1 = 37,8$ см
Опыт 2: $d_2 = 30,0$ см, $f'_2 = 30,2$ см
Опыт 3: $d_3 = 40,0$ см, $f'_3 = 23,8$ см
Перевод в систему СИ:
$d_1 = 0,250$ м, $f'_1 = 0,378$ м
$d_2 = 0,300$ м, $f'_2 = 0,302$ м
$d_3 = 0,400$ м, $f'_3 = 0,238$ м
Приборная погрешность измерения расстояний (цена деления линейки 1 мм) $\Delta d_{приб} = \Delta f'_{приб} = 0,1$ см $= 0,001$ м.
Найти:
Фокусное расстояние линзы $\text{F}$ и его погрешность $\Delta F$.
Решение:
Для определения фокусного расстояния собирающей линзы воспользуемся формулой тонкой линзы, выразив из неё $\text{F}$:
$ F = \frac{d \cdot f'}{d + f'} $
1. Вычисление фокусного расстояния для каждого опыта:
Опыт 1:
$ F_1 = \frac{d_1 \cdot f'_1}{d_1 + f'_1} = \frac{0,250 \cdot 0,378}{0,250 + 0,378} = \frac{0,0945}{0,628} \approx 0,1505 $ м
Опыт 2:
$ F_2 = \frac{d_2 \cdot f'_2}{d_2 + f'_2} = \frac{0,300 \cdot 0,302}{0,300 + 0,302} = \frac{0,0906}{0,602} \approx 0,1505 $ м
Опыт 3:
$ F_3 = \frac{d_3 \cdot f'_3}{d_3 + f'_3} = \frac{0,400 \cdot 0,238}{0,400 + 0,238} = \frac{0,0952}{0,638} \approx 0,1492 $ м
2. Вычисление среднего значения фокусного расстояния:
$ F_{ср} = \frac{F_1 + F_2 + F_3}{3} = \frac{0,1505 + 0,1505 + 0,1492}{3} = \frac{0,4502}{3} \approx 0,1501 $ м
3. Расчёт абсолютной погрешности измерений:
Найдём абсолютные отклонения для каждого измерения (случайная погрешность):
$ \Delta F_1 = |F_{ср} - F_1| = |0,1501 - 0,1505| = 0,0004 $ м
$ \Delta F_2 = |F_{ср} - F_2| = |0,1501 - 0,1505| = 0,0004 $ м
$ \Delta F_3 = |F_{ср} - F_3| = |0,1501 - 0,1492| = 0,0009 $ м
Средняя абсолютная случайная погрешность:
$ \Delta F_{случ} = \frac{\Delta F_1 + \Delta F_2 + \Delta F_3}{3} = \frac{0,0004 + 0,0004 + 0,0009}{3} \approx 0,0006 $ м
Оценим приборную погрешность для второго опыта (как наиболее близкого к случаю $d=f'=2F$, где погрешность минимальна):
$ \Delta F_{приб} = F_{ср}^2 \left( \frac{\Delta d_{приб}}{d_2^2} + \frac{\Delta f'_{приб}}{(f'_2)^2} \right) \approx (0,1501)^2 \left( \frac{0,001}{(0,300)^2} + \frac{0,001}{(0,302)^2} \right) \approx 0,0225 \left( 0,0111 + 0,0110 \right) \approx 0,0005 $ м
Полная абсолютная погрешность равна сумме случайной и приборной погрешностей:
$ \Delta F = \Delta F_{случ} + \Delta F_{приб} \approx 0,0006 + 0,0005 = 0,0011 $ м
Округлим погрешность до одной значащей цифры: $ \Delta F \approx 0,001 $ м. Тогда результат для среднего значения фокусного расстояния округляем до того же десятичного знака:
$ F_{ср} = 0,150 $ м
Окончательный результат запишем в виде $ F = F_{ср} \pm \Delta F $:
$ F = (0,150 \pm 0,001) $ м, или $ F = (15,0 \pm 0,1) $ см.
4. Расчёт относительной погрешности:
$ \varepsilon = \frac{\Delta F}{F_{ср}} \cdot 100\% = \frac{0,001}{0,150} \cdot 100\% \approx 0,7\% $
Так как относительная погрешность мала, результат можно считать достоверным.
Ответ: Фокусное расстояние линзы, определённое экспериментально, составляет $ F = (15,0 \pm 0,1) $ см. Относительная погрешность измерений составила примерно $0,7\%$.
Другие задания:
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