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The image of an object, formed by a plano-convex lens at a distance of 8m 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 the wavelength in free space. The radius of the curved surface of the lens is

(a) 1 m
(b) 6 m
(c) 5 m
(d) 3 m
in Physics
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+1 vote

Correct option is d) 3m

Explaination::

$$\mu ={\lambda_0\over \lambda_m}={3\over2}$$

$${1\over f}={(\mu-1)\over R}={1\over 2R}$$

$${1\over f}={1\over V}-{1\over u}$$

$${1\over8}-({1\over24})={1\over2R}$$

$${3+1\over24}={1\over2R}$$

by (5.4k points)
R=3
hence , option d) is correct