A plano-convex lens becomes an optical system of 28 cm focal length when its plane surface is silvered and illuminated from left to right as shown in fig - A If the same lens is instead silvered on the curved surface and illuminated from another side as in fig- B , it acts as an optical system of focal length 10 cm . The refractive index of the material of the lens is:

Step-by-step solution

Case-1 1 f 1 = ( μ − 1 ) R , f = - 28 ⇒ P = 2 p 1 + p 2 ⇒ 1 28 = 2 μ - 1 R Case-2 1 f 1 = ( μ − 1 ) R ,   f 2 = R 2  , f  = − 10   cm ⇒ P = 2 P 1 + P 2 ⇒ 1 10 = 2 μ - 1 2 + 2 R ⇒ 1 10 = 2 28 + 2 R 2 R = 1 10 - 2 28 = 18 280 ⇒ R = 280 9   cm ⇒ 1 28 = 2 μ - 1 280 9 μ - 1 = 5 9 ⇒ μ = 1 + 5 9 = 14 9 = 1.55 .