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Консультация № 179467
12.07.2010, 11:16
0.00 руб.
0
2
1
Здравствуйте,
Предмет находится на расстоянии L=90 см от экрана. Между предметом и экраном перемещают линзу, причем при одном положении линзы на экране получается увеличенное изображение предмета, а при другом — уменьшенное. Каково фокуснс$е расстояние линзы, если линейные размеры первого изображения в четыре раза больше размеров второго?
Предмет находится на расстоянии L=90 см от экрана. Между предметом и экраном перемещают линзу, причем при одном положении линзы на экране получается увеличенное изображение предмета, а при другом — уменьшенное. Каково фокуснс$е расстояние линзы, если линейные размеры первого изображения в четыре раза больше размеров второго?
Обсуждение
12.07.2010, 17:52
общий
это ответ
Здравствуйте, max123.
Система
1/d+1/f=1/F
d+f=L
имеет 2 симметричных решения.
Учитывая, что отношение размеров объекта и изображения равно отношению их расстояний от линзы (доказывается через подобные треугольники, образованные лучами, идущими через оптический центр), делаем выводы:
отношение размеров уменьшенного изображения и объекта равно отношению размеров объекта и увеличенного изображения
изображения в 2 раза больше/меньше объекта
линза делит расстояние L в отношении 2:1
d=30см, f=60см или наоборот
F=1/(1/d+1/f)=1/(1/0,3+1/0,6)=1/5=0,2м=20 см
Система
1/d+1/f=1/F
d+f=L
имеет 2 симметричных решения.
Учитывая, что отношение размеров объекта и изображения равно отношению их расстояний от линзы (доказывается через подобные треугольники, образованные лучами, идущими через оптический центр), делаем выводы:
отношение размеров уменьшенного изображения и объекта равно отношению размеров объекта и увеличенного изображения
изображения в 2 раза больше/меньше объекта
линза делит расстояние L в отношении 2:1
d=30см, f=60см или наоборот
F=1/(1/d+1/f)=1/(1/0,3+1/0,6)=1/5=0,2м=20 см
5
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