Question

The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will ______.

विकल्प

• act as a convex lens only for the objects that lie on its curved side.

• act as a concave lens for the objects that lie on its curved side.

• act as a convex lens irrespective of the side on which the object lies.

• act as a concave lens irrespective of side on which the object lies.

Answer 1

The radius of curvature of the curved surface of a plano-convex lens is 20 cm. If the refractive index of the material of the lens be 1.5, it will act as a convex lens irrespective of the side on which the object lies.

Explanation:

If object lies on curved side then R₁ = +20 cm and R₂ = `oo`, μ₁ = 1, μ₂ = 1.5

`1/f = (mu_2 - mu_1) (1/R_1 - 1/R_2)`

`1/f = (1.5 - 1) (1/20 - 1/oo) = 0.5/20 = 5/200 = 1/40`

F = + 40 cm

If object lies on plane side R₁ = `oo` and R₂ = – 20 cm, μ₁ = 1, μ₂ = 1.5

`1/f = (mu_2 - mu_1) (1/R_1-1/R_2)`

`1/f = (1.5 - 1)(1/oo - (- 1/20)) = 0.5 xx (+ 1/20)`

`1/f = 5/200`

f = + 40 cm

So, lens will always act as a convex lens irrespective of the side on which objects lie.