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 is free space. The radius of the curved surface of the lens is

Options

A. 1m
B. 2m
C. 3m
D. 6m

Answer

C

Explanation

Real image `implies v = +8 m`
`m = (v)/(u) = -(1)/(3) implies u = -24m`
` f = (uv)/(u-v) = ((-24)(8))/(-24-8) = 6 m`
for plano convex lens
`(1)/(f) = (u-1) ((1)/(R) - (1)/(oo)) implies (1)/(6) = ((3)/(2) -1) ((1)/(R)) implies R = 3 m `