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Консультация № 179492
14.07.2010, 02:16
0.00 руб.
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2
1
Здравствуйте,
Сложный объектив состоит из двух тонких линз: собирательной с фокусным расстоянием F, =20 см и рассеивающей — с F2 = —10 см. Линзы расположены на расстоянии l = 15 см друг от друга. С помощью объектива получают иа экране изображение Солнца. Какое фокусное расстояние F должна иметь тонкая линза, чтобы изображение Солнца, полученное с ее помощью, имело такой же размер?
Сложный объектив состоит из двух тонких линз: собирательной с фокусным расстоянием F, =20 см и рассеивающей — с F2 = —10 см. Линзы расположены на расстоянии l = 15 см друг от друга. С помощью объектива получают иа экране изображение Солнца. Какое фокусное расстояние F должна иметь тонкая линза, чтобы изображение Солнца, полученное с ее помощью, имело такой же размер?
Обсуждение
14.07.2010, 19:33
общий
это ответ
Здравствуйте, max123.
Решение:
Пусть α – угловой размер Солнца. Изображение Солнца, даваемое первой линзой, находится в ее фокальной плоскости и имеет размер (с учетом малости α)
h1= - αF1
Расстояние от этого изображения до второй линзы
d = l - F1
Из формулы линзы
1/(l-F1)+1/f=1/F2
находим расстояние между экраном и линзой Л2:
f=F2*(l-F1)/(l-F1-F2)
Тогда размер второго изображения равен
h2=-α*F1*f/d=-α*F1*F2/(l-F1-F2)
Если используется одинокая тонкая линза с фокусным расстоянием F, то размер изображения Солнца в ней составляет
h2=αF
Окончательно для фокусного расстояния этой линзы получаем
F=-F1*F2/(l-F1-F2)
Подставляем числовые значения:
F=-20*(-10)/(15-20+10)=-(-200)/5=40см
Ответ: F=40 см.
Решение:
Пусть α – угловой размер Солнца. Изображение Солнца, даваемое первой линзой, находится в ее фокальной плоскости и имеет размер (с учетом малости α)
h1= - αF1
Расстояние от этого изображения до второй линзы
d = l - F1
Из формулы линзы
1/(l-F1)+1/f=1/F2
находим расстояние между экраном и линзой Л2:
f=F2*(l-F1)/(l-F1-F2)
Тогда размер второго изображения равен
h2=-α*F1*f/d=-α*F1*F2/(l-F1-F2)
Если используется одинокая тонкая линза с фокусным расстоянием F, то размер изображения Солнца в ней составляет
h2=αF
Окончательно для фокусного расстояния этой линзы получаем
F=-F1*F2/(l-F1-F2)
Подставляем числовые значения:
F=-20*(-10)/(15-20+10)=-(-200)/5=40см
Ответ: F=40 см.
5
Форма ответа
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