Question

На каком расстоянии от рассеивающей линзы находится предмет если его изображение получается на расстоянии 2 см от неё фокусное расстояние этой линзы 7 см

Answer 1

F=7 см     f=2 см    d=?
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Для рассеивающей линзы
-1/F=1/d-1/f
d=f*F/(F-f)=2*7/(7-2)=2.8 см
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Answer 2

Calculating Object Distance from a Diverging Lens

To calculate the distance of the object from a diverging lens when its image is formed at a distance of 2 cm from it, and the focal length of the lens is 7 cm, we can use the lens formula:

Lens Formula: The lens formula is given by: \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Where: - \( f \) = focal length of the lens - \( v \) = image distance - \( u \) = object distance

Given: - Focal length (\( f \)) = 7 cm - Image distance (\( v \)) = -2 cm (negative because the image is formed on the same side as the object for a diverging lens)

Calculating Object Distance (\( u \)): Using the lens formula, we can rearrange it to solve for \( u \): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] \[ \frac{1}{u} = \frac{1}{v} - \frac{1}{f} \] \[ \frac{1}{u} = \frac{1}{-2} - \frac{1}{7} \] \[ \frac{1}{u} = -\frac{7}{14} - \frac{2}{14} \] \[ \frac{1}{u} = -\frac{9}{14} \] \[ u = -\frac{14}{9} \] \[ u \approx -1.56 \, cm \]

Answer: The object is approximately 1.56 cm from the diverging lens.

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