NCERT Physics Class 12 Exemplar Ch 9 Ray Optics and Optical Instruments Part 2
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Q 25. In many experimental setups the source and screen are fixed at a distance say D and the lens is movable. Show that there are two positions for the lens for which an image is formed on the screen. Find the distance between these points and the ratio of the image sizes for these two points.
Ans:
From the reversibility of u and v, as seen from the formula for lens,

It is clear that there are two positions for which there shall be an image on the screen.

Let the first position be when the lens is at O.
Given
Placing it in the lens formula
Thus, if the object distance isthen the image is at

If the object distance isthen the image is at

The distance between the poles for these two object distances is
Let
If then the image is at
∴The magnification
ifthen
∴The magnification Thus