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Q.

The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times and the wavelength in free space. The radius of the curved surface of the lens is

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a

1 m

b

2 m

c

3 m

d

6 m

answer is C.

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Detailed Solution

μ=λairλmedium=12/3=32 Further, m=13=vu ∴v=u3v=+8m (Real image ) Given⇒u=−24m (Real object) Now, 1v−1u=1f=μ−11+R−1∞∴18+124=32−11R ∴R=3 m
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The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is one-third the size of the object. The wavelength of light inside the lens is 2/3 times and the wavelength in free space. The radius of the curved surface of the lens is