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Question:

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 :

2 m

1 m

3 m

6 m

Solution:

Refractive index, μ = λ/λm = 3/2
Magnification, m = -v/u = -1/3
Since the image is real, v = 8m
Therefore, u = 3v = 24m
Using lens formula,
1/v - 1/u = (μ-1)/R
1/8 - 1/(-24) = (3/2 - 1)/R
(3+1)/24 = 1/2R
4/24 = 1/2R
1/6 = 1/2R
R = 3m