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Question

Two thin converging lenses are placed on a common axis, so that the center of one of them coincides with the focus of the other. An object is placed at a distance twice the focal length from the left-hand lens. Where will its image be? What is the lateral magnification? The focal length of each lens is f.

A
0.25
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B
0.5
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C
0.75
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D
1
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Solution

The correct option is B 0.5

The image formed by first lens will be at a distance 2f with lateral magnification m1=1.
For the second lens this image will behave as a virtual object.
Using the lens formula,
1v1u=1f we have, for u=f
1v1f=1f v=f2
m2=v2u2=(f/2)f=12
Therefore, final image is formed at a distance f2 from the second lens with total lateral magnification,
m=m1×m2=(1)×(12)=12

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