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Консультация № 199879
15.12.2020, 09:50
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Здравствуйте! Прошу помощи в следующем вопросе:
Расстояние от лампочки до экрана на оптической скамье 1 м. На каком расстоянии от лампочки нужно поставить собирающую линзу с фокусным расстоянием 24 см, чтобы получить на экране резкое изображение лампочки?
Расстояние от лампочки до экрана на оптической скамье 1 м. На каком расстоянии от лампочки нужно поставить собирающую линзу с фокусным расстоянием 24 см, чтобы получить на экране резкое изображение лампочки?
Обсуждение
18.12.2020, 19:46
общий
это ответ
Здравствуйте, ira.medvedeva00!
Дано:
r=1 м
F=0.24 м
Найти: d
Решение:
1. Формула тонкой линзы
1/f+1/d=1/F (1) - здесь f - расстояние от линзы до изображения;
2. По условию:
f+d=r (2)
Из условия (2) выражаем f и подставляем в (1). Получаем
(d+(r-d))/((r-d)*d) = 1/F
После несложных преобразований получаем квадратное уравнение
d2-rd+rF=0,
два корня которого вполне себе действительные и согласующиеся с условием задачи,
d1=0,4 м
d2=0,6 м
Таким образом, линзу можно установить либо на расстоянии 40 см, либо 60 см от лампочки. В обоих случаях получим резкое изображение: в первом случае увеличенное, во втором - уменьшенное.
Удачи
Дано:
r=1 м
F=0.24 м
Найти: d
Решение:
1. Формула тонкой линзы
1/f+1/d=1/F (1) - здесь f - расстояние от линзы до изображения;
2. По условию:
f+d=r (2)
Из условия (2) выражаем f и подставляем в (1). Получаем
(d+(r-d))/((r-d)*d) = 1/F
После несложных преобразований получаем квадратное уравнение
d2-rd+rF=0,
два корня которого вполне себе действительные и согласующиеся с условием задачи,
d1=0,4 м
d2=0,6 м
Таким образом, линзу можно установить либо на расстоянии 40 см, либо 60 см от лампочки. В обоих случаях получим резкое изображение: в первом случае увеличенное, во втором - уменьшенное.
Удачи
Об авторе:
С уважением
shvetski
С уважением
shvetski
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