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Question

# An object is placed 30cm away from a convex lens of focal length 10cm and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by 45cm to get a sharp image again. The magnitude of focal length of the concave lens is (in cm):

A
72
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B
60
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C
36
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D
20
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Solution

## The correct option is D 20Given : u=−30cm f′=10cmConvex lens forms an image at point I′.Using lens formula 1v′−1u=1f′ 1v′−1−30=110 ⟹ v′=15 cmLet the focal length of the combination of the two lenses be F which forms an image at I.II′=45 cm⟹ v=v′+II′=15+45=60 cmUsing lens formula for the combination 1v−1u=1F 160−1−30=1F ⟹ F=20 cmLet the focal length of the concave lens be f′′Using the focal length formula for combination of lenses 1F=1f′+1f′′ 120=110+1f′′ ⟹f′′=−20 cmHence the magnitude of focal length of the concave lens is 20 cm

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