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Question

A screen is placed 90 cm away from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by 20 cm. Find the focal length of lens.

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Solution

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The image of the object can be located on the screen for two-position of convex lens such that u and v are exchanged.

The separation between two positions of the lens is, d= 20 cm

From the figure,

u1+v1=90cm

v1−u1=20cm

Solving,

v1=55cm, u1=35cm

From lens formula,

1v−1u=1f

155−1−35=1f

⇒1f=155+135=55×3590

⇒f=21.4cm

⇒f=21.4cm

Hence, the correct option is (B)

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