The image of an object, formed by a plano - convex lens at a distance of 8 m behind the lens, is real and is…

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 the wavelength in free space. The radius of the curved surface of the lens is
  1. 1 m
  2. 2 m
  3. 3 m
  4. 6 m

Solution

V = 8m
Magnification = v u = - 1 3
u = -24
also μ = c V m = λ a λ m = 3 2
1 f = μ - 1 1 R 1 - 1 R 2 ​
1 f = μ - 1 1 ∞ - 1 - R
1 f = 3 2 - 1 1 R
f = 2R
from lens formula
1 v - 1 u = 1 f
1 8 + 1 2 4 = 1 2R
4 24 = 1 2R
⇒ R = 3 m

Asked in: JEE Advanced 2013 (Paper 1)

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