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.ย
A
42.8 cm
B
21.4 cm
C
10.7 cm
D
5.5 cm
Medium
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Solution
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Correct option is B)
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,
u1โ+v1โ=90cm
v1โโu1โ=20cm
Solving,
v1โ=55cm,ย u1โ=35cm
From lens formula,
v1โโu1โ=f1โย
551โโโ351โ=f1โ
โf1โ=551โ+351โ=9055ร35โ โf=21.4cm
Hence, the correct option is (B)
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