Question

A plano concave lens forms a virtual image at a distance of 5 cm in front of the lens of an object placed in front of it. 

The image formed is 1/2 times the size of the object. If the speed of light in the Plano concave lens is 2/3 times the speed of light in air, then find 

(a) the refractive index of the lens. 

(b) the radius of curvature of the curved surface of the lens.

Answer 1

(a) Refractive index = c/v

n = c /(2/3c) =1.5 

(b) v = - 5.0 cm

m = v/u = h_i/h_o 

-5/u = (1/2h_o)/h_o 

u = - 5 × 2 = -10 cm

1/f = 1/v - 1/u 

1/f = -1/5 + 1/10 = -1/10 

f = - 10 cm 

By lens maker formula 

1/f = (n - 1)(1/R₁ - 1/R₂) 

\(-1/10 = (1.5 - 1)(1/R_1 - 1/-∞)\)  

R₁ = - 10 × 0.5 cm = - 5 cm