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
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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
Hence, the correct option is (B)
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