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Консультация № 189072
03.04.2016, 14:21
0.00 руб.
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Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Между двумя тонкими стеклянными клиньями с одинаковыми углами при вершине и показателями преломления n1 и n2 соответственно помещают третий клин так, что они образуют плоскопараллельную пластинку (рис. 7-вложение). Пучок параллельных лучей света, падающих на такую систему, не отклоняется. Вычислите показатель преломления n3 среднего клина.
Между двумя тонкими стеклянными клиньями с одинаковыми углами при вершине и показателями преломления n1 и n2 соответственно помещают третий клин так, что они образуют плоскопараллельную пластинку (рис. 7-вложение). Пучок параллельных лучей света, падающих на такую систему, не отклоняется. Вычислите показатель преломления n3 среднего клина.
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Обсуждение
06.04.2016, 16:13
общий
это ответ
Здравствуйте, anton74551!
Из геометрических соображений находим
[$947$]1+[$947$]2=2[$945$]
по закону преломления
n1sin[$945$]=n3sin[$947$]1
n2sin[$945$]=n3sin[$947$]2
(n1+n2)sin[$945$]=n3(sin[$947$]1+sin[$947$]2)
(n1+n2)sin[$945$]=2n3sin(([$947$]1+[$947$]2)/2)[$183$]cos(([$947$]1-[$947$]2)/2)
(n1+n2)sin[$945$]=2n3sin[$945$][$183$]cos(([$947$]1-[$947$]2)/2)
(n1+n2)/2=n3cos(([$947$]1-[$947$]2)/2)
Если [$947$]1-[$947$]2 достаточно мало (малые углы [$945$] либо мало различающиеся коэффициенты преломления), то
cos(([$947$]1-[$947$]2)/2)[$8776$]1
и тогда получаем
n3=(n1+n2)/2
Примечание: при необходимости более точного численного решения (особенно при существенном отклонении луча в среднем клине) поправку на cos(([$947$]1-[$947$]2)/2) можно ввести с помощью итерации (найдя углы преломления для значения n3 предыдущего шага).
Из геометрических соображений находим
[$947$]1+[$947$]2=2[$945$]
по закону преломления
n1sin[$945$]=n3sin[$947$]1
n2sin[$945$]=n3sin[$947$]2
(n1+n2)sin[$945$]=n3(sin[$947$]1+sin[$947$]2)
(n1+n2)sin[$945$]=2n3sin(([$947$]1+[$947$]2)/2)[$183$]cos(([$947$]1-[$947$]2)/2)
(n1+n2)sin[$945$]=2n3sin[$945$][$183$]cos(([$947$]1-[$947$]2)/2)
(n1+n2)/2=n3cos(([$947$]1-[$947$]2)/2)
Если [$947$]1-[$947$]2 достаточно мало (малые углы [$945$] либо мало различающиеся коэффициенты преломления), то
cos(([$947$]1-[$947$]2)/2)[$8776$]1
и тогда получаем
n3=(n1+n2)/2
Примечание: при необходимости более точного численного решения (особенно при существенном отклонении луча в среднем клине) поправку на cos(([$947$]1-[$947$]2)/2) можно ввести с помощью итерации (найдя углы преломления для значения n3 предыдущего шага).
5
Cпасибо огромное за помощь!
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