• Ср. Июн 7th, 2023

Дисперсия света и цвета тел

Дисперсия света и цвета тел

Дисперсия света и цвета тел

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

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Дисперсия света и цвета тел
Дисперсия света и цвета тел

Дисперсия света и цвета тел. Задачки

842. Луч белого света падает под углом а= 30° на призму, преломляющий угол которой равен <р=45°. Определить
угол -0 между крайними лучами спектра по выходе нз
призмы, если показатели преломления стекла призмы для
крайних лучей видимого спектра равны ик=1,62, иф= 1,67.

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

843. На двояковыпуклую линзу, радиусы кривизны поверхностей которой равны R i= R 2=40 см, падает белый свет
от точечного источника, расположенного на оптической оси
линзы на расстоянии а= 50 см от нее. Вплотную перед линзой
расположена диафрагма диаметра D =1 см, ограничивающая
поперечное сечение светового пучка. Показатели преломления для крайних лучей видимого спектра равны пк=1,74
и Яф—1,8. Какую картину можно будет наблюдать на экране, расположенном на расстоянии Ь—50 см от линзы перпендикулярно ее оптической оси?
844. Используя результаты задачи 783, построить элементарную теорию радуги, т. е. показать, что центр радуги
находится на прямой, проведенной от Солнца через глаз
наблюдателя, и что дуга радуги представляет собой часть
окружности, все точки которой видны под углом 42° (для
красного света) по отношению к прямой, соединяющей глаз
наблюдателя й центр радуги.

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

845. Объяснить качественно причины появления двойной радуги. Каково чередование цветов в первой (основной)
и,второй радуге?
846. Можно ли в Москве во время летнего солнцестояния (22 июня) наблюдать радугу в полдень? (В это время
Солнце в северном полушарии стоит наиболее высоко над
горизонтом.)
847. Длина волны в воде уменьшается в п раз, где п —
показатель преломления. Означает ли это, что ныряльщик
не может видеть окружающие тела в естественном цвете?
848. На тетради написаны красным карандашом «отлично» и зеленым «хорошо». Имеются два стекла — зеленое и красное. Через какое стекло надо смотреть, чтобы увидеть оценку «отлично»?
849. Почему объективы с «просветленной оптикой» (см.
задачу 820) имерт пурпурно-фиолетовый (сиреневый) оттенок? .
850. Цвета тонких пленок (например, пленки нефти на
воде) и цвета радуги имеют совершенно различные оттенки,
Почему?

161 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

851. Тонкая мыльная пленка натянута на вертикальную
рамку. При освещении белым светом на пленке наблюдаются
три цветные полосы: пурпурного’ (малинового), желтого и
_ голубого (сине-зеленого) цветов. Найти расположение и
порядок полос.
852. Почему днем Луна имеет чистый белый цвет, а
после захода Солнца принимает желтоватый оттенок?
853. Почему столб дыма, поднимающегося над крышами
домов, на темном фоне окружающих предметов кажется .
синим, а на фоне светлого неба — желтым или даже крас*
новатым?
854. Почему цвета влажных предметов кажутся более
глубокими, более насыщенными, чем сухих?

162 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Дисперсия света и цвета тел. Ответочки

842. Как показано в задаче 730, угол падения а, преломляющий
угол призмы q> н показатель преломления и связаны с углом Р, под
которым луч выходит из призмы, выражением

411 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Отсюда для sin (5 получаем следующее уравнение:
sin a sfn» sin^p (l’+ ctg* ф)+ 2 sin р -т- sm® а
sin <р tg <p r sin2 ср
или (при данных значениях а и f)
2 sin 2P-f- V 2 s i n p + i — — r t 2 = 0.
= ©,
Решая это уравнение, найдем
sin р = —1 ± V 4я2 — 1
2 |/2

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Физический смысл имеет решение со знаком плюс. Для красных лучей
sin рк я 0,26. Следовательно, рк я; 15°6′. Для фиолетовых sin Р* я 0,31
и Рф « 18°6′. Искомый угол 6 = Рф — Рк ~ 3°. ;
— 843. Для красных лучей фокусное расстояние линзы /к =
== Р/2(пк — 1) ~ 27 см; для фиолетовых /ф = 25 см. По формуле линзы
изображение, даваемое красными лучами, будет расположено ва расстоянии Ьк^= afK/(a— fB)= 5 8 ,7 см; фиолетовыми—на расстоянии
&ф==50 см. ■ :
На экране (рис. 564) изображение источника будет иметь форму
пятна, края которого окрашены в красный цвет. Диаметр пятна а
d =

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

844. Солнечные лучи, падающие на капли дождя, можно считать
параллельным!}. По выходе из капли после однократного отражения
на внутренней поверхности капли лучи расходятся по всем направлениям. Лишь лучи, испытавшие наименьшее отклонение, идут приблизительно параллельно. Поэтому именно эти лучи, попадая в глаз,
вызовут наибольшее зрительное впечатление.’ Эти лучи идут, так
сказать, с наибольшей «плотностью». Остальные лучи рассеиваются
во все стороны. Для параллельных лучей угол отклонения, как
показано в_ задаче 783, равен 138°. Следовательно, угол между падающими от Солнца лучами и направлением ва радугу составляет 42°
(для красного света) (рис. Б65).
В глаз попадает свет от тех капель, которые находятся в направлении, составляющем угол 42° с линией, проверенной через

412 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

глаз в С о т к е . ‘Для’- -ja w . еасгавляег’вримерно 40°. ‘■
845. Первая (основная) радуга наблюдается благодаря лучам,
испытавшим одно отражение внутри капелек воды. При преломлении
наиболее сильно отклоняются от первоначального направления фиолетовые лучи (см. задачу 782) (/_ 0 растет с ростом п, так как г
уменьшается), поэтому внешняя дуга будет красной, а внутренняя —
фиолетовой.

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Вторая радуга вызвана лучами, испытавшими два отражения
внутри капёлек. Примерный ход луча изображен на рис. 566. Направление на радугу составляет, как можно показать, 51° с линией,
соединяющей глаз и Солнце. Чередование цветов при двух преломлениях и двух отражениях получается обратным: внешняя- дуга будет
фиолетовой, а внутренняя—красной. После двух отражений интенсивность света оказывается сильно ослабленной, вследствие чего вторая радуга бывает гораздо менее интенсивной, чем первая.
846. Географическая широта Москвы, т. е. угол между плоскостью
экватора и нормалью к поверхности земного шара, ф = 56°. Солнце
в этот момент стоит в зените над северным тропиком (широта а = 23,5°).
Следовательно, угол между направлением на Солнце и горизонтом
(рис. 567)

413 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Радуга же может быть видна только в том случае, когда высота
Солнца над горизонтом не превышает 42° (см. рис. 565). Следовнтел-ьио,
наблюдать радугу в указанное время нельзя. ‘
847. Наш глаз получает ощущение того или иного цвета, когда
его чувствительные элементы раздражаются световой волной определенной частоты. Частота же световых волн не меняется при переходе
из одной среды в другую. .
848. Необходимо смотреть через зеленое стекло. При этом надпись
будет видна черной на зеленом фоне бумаги, так как красный свет
надписи «отлично» не пропускается зеленым стеклом. При рассматривании через красное стекло красная надпись не будет видна на
красном фоне бумаги.

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

849. Объектив преимущественно отражает крайние части видимого
спектра: красную и фиолетовую (см. задачу 820). От смешения этих
цветов возникает сиреневый оттенок.
860. Цвета радуги являются чистыми спектральными цветами
(см. задачу 844), так как по данному направлению виден лишь луч
вполне определенной длины волны. Цвета тонких пленок, наоборот,
получаются из-за гашения (полного или частичного) лучей некоторого
спектрального интервала в результате интерференции. Цвет пленки
будет дополнительным к цвету этого спектрального интервала.

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

851. Под действием силы тяжести мыльная вода стекает в нижнюю часть пленки, которая всегда толще, чем верхняя. Следовательно,
полосы, которые указывают геометрическое место точек одинаковой
толщины, должны быть расположены горизонтально. Голубой (синезеленый) оттенок получается при исключении из полного спектра его
длинноволновой (красно-ораижевой) части (см. задачу 850). При
гашении средней (зеленой) части спектра оставшиеся лучи придают
пленке пурпурный (малиновый) оттенок, а при вычитании из сплошного спектра его коротковолновой (сине-фиолетовой), части плевка
выглядит желтой. Если разность хода взаимно гасящихся лучей
составляет одно и то же число полуволн во всех трех случаях, то
вверху должна быть желтая полоса, затем пурпурная и внизу голубая.

414 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

882. .Днем- рассеянный’ небом голубой свет добавляется к желтоватому свету самой Луны. Это смешение цветов воспринимается
глазом как белый цвет. После захода Солнца голубой свет неба
•ослабевает и Луна принимает желтоватый оттенок.
853. На темном фоне мы видим дым вследствие того, что он рассеивает падающие на него сверху солнечные лучи. Частицы дыма
рассеивают синий свет гораздо сильнее, чем красный или желтый.
Поэтому цвет дыма кажется синим.
На фоне светлого неба дым виден в проходящем свете. Дым
кажется желтоватым, так как синий свет рассеивается во все стороны и только длинноволновый участок спектра белого света достй-
• гаёт глаз.
854, Тонкая пленка воды, покрывающая влажный предмет, отражает падающий белый свет по одному определенному направлению.
Поверхность предмета уже не рассеивает белый свет во все стороны,
и господствующим становится его собственный цвет. Рассеянный свет
не налагается на отраженный от предмета, и поэтому цвет кажется
более насыщенным.

415 Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Буховцев Борис Борисович, Кривченков Владим ир Дмитриевич,
Мякишев Геннадий Яковлевич, Сараево И рина Макаровна
СБОРНИК ЗАДАЧ ПО ЭЛЕМ ЕНТАРНОЙ Ф ИЗИКЕ
М., 1974 г., 416 стр. с илл.
Редактор Б . Ю. К.оган *
Техн. редактор В. Н. Кондакова
Корректоры Т. С. Плетнева, Л . С. Сомова

 

Глава V. ГЕОМЕТРИЧЕСКАЯ ОПТИКА. Дисперсия света и цвета тел.

Сдано в набор 10/V1 1974 Г: Подписано к печати 30/1Х 1974 г.
Бумага 84X108*/»*. тип. .V 3. Физ. печ. л. 13. Условн. печ.
л. 21,84. Уч.-изд. д. 23.02. Тираж 400 ООО экз. (2-й завод
150 001’—400 000). Цена книги / z коп. Заказ Na 1472 .
Издательство «Наука»
Главная редакция физико-математической литературы
117071, Москва, В-71, Ленинский проспект, 15
Ордена Трудового Красного Знамени
П ервая Образцовая типография имени А. А. Жданова
Союзполиграфпрома при Государственном комитете ‘
Совета Министров СССР по делая издательств,
полиграфии и книжной торговли;
М осква, М -54, В ал о в ая, 28

416

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