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Консультация № 143780
13.09.2008, 10:09
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Доброго времени суток уважаемые эксперты...
Вот такая задачка:
Радиус кривизны вогнутого сферического зеркала 20 см. На растоянии 30 см от зеркала поставлен предмет высотою 1 см. Найти положение и высоту изображения.
Заранее спасибо!!!
Вот такая задачка:
Радиус кривизны вогнутого сферического зеркала 20 см. На растоянии 30 см от зеркала поставлен предмет высотою 1 см. Найти положение и высоту изображения.
Заранее спасибо!!!
Обсуждение
15.09.2008, 09:45
общий
это ответ
Здравствуйте, Баженов Павел Андреевич!
Когда пучок параллельных лучей падает на вогнутое сферическое зеркало, отражённые лучи пересекаются в точке, расположенной на половине расстояния между зеркалом и центром его кривизны. Эта точка называется фокусом зеркала, а расстояние между зеркалом и этой точкой (равное половине радиуса кривизны) – фокусным расстоянием. Расстояние s от предмета до зеркала, расстояние sи от зеркала до изображения и фокусное расстояние f связаны формулой: 1/f = (1/s) + (1/sи) (1). (См. здесь). Отсюда получается выражение для sи: sи = s*f/(s - f) (2). Высота изображения hи находится по формуле: hи = hп*sи/s (3), где hп - высота предмета. В нашем случае: f = 20/2 = 10 см; sи = 30*10/(30 - 10) = 15 см; hи = 1*15/30 = 0.5 см.
Когда пучок параллельных лучей падает на вогнутое сферическое зеркало, отражённые лучи пересекаются в точке, расположенной на половине расстояния между зеркалом и центром его кривизны. Эта точка называется фокусом зеркала, а расстояние между зеркалом и этой точкой (равное половине радиуса кривизны) – фокусным расстоянием. Расстояние s от предмета до зеркала, расстояние sи от зеркала до изображения и фокусное расстояние f связаны формулой: 1/f = (1/s) + (1/sи) (1). (См. здесь). Отсюда получается выражение для sи: sи = s*f/(s - f) (2). Высота изображения hи находится по формуле: hи = hп*sи/s (3), где hп - высота предмета. В нашем случае: f = 20/2 = 10 см; sи = 30*10/(30 - 10) = 15 см; hи = 1*15/30 = 0.5 см.
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