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.

A
42.8 cm
B
21.4 cm
C
10.7 cm
D
5.5 cm
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 cmFrom the figure,u1+v1=90cmv1−u1=20cmSolving,v1=55cm, u1=35cmFrom lens formula,1v−1u=1f 155−1−35=1f⇒1f=155+135=55×3590⇒f=21.4cmHence, the correct option is (B)

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