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618.


Problem 44.25 (RHK)

A luminous object and a screen are a fixed distance D apart. (a) We have to show that a converging lens of focal length f will form a real image on the screen for two positions of the object that are separated by

(b) We have to show that the ratio of the two image sizes for these two positions is


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 For answering this problem we will use the thin lens formula

and the expression for the lateral magnification

where is the object distance, the image distance and f the focal length of the lens.

(a)

As we are considering real image formed by the lens, the image distance, , will be positive. The object distance, , will be , as the object is at a distance D from the screen where the image is formed. Let the focal length of the converging lens be f. We thus have the equation

The roots of this quadratic equation are

The object distances for the two image positions will therefore be

We thus find that the distance between the two object positions for which real images are formed on the screen will be

(b)

The ratio of the two image sizes for these two positions of the object will therefore be