Question

A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.when its curved surface is silvered and the plane surface not silvered,it is equivalent to a concave mirror of focal length 10cm,then the refractive index of the material of the lens is

Answer 1

Given:

A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.

To find:

The refractive index of the material of the lens is

Solution:

Let fm be the focal length of the silvered surface.

A plano-convex lens, when silvered at its plane surface is equivalent to a concave mirror of focal length 28cm.

∴ fm = ∞

Thus, 1/28 = 2/f1 + 1/fm

1/28 =2/f1 + 0

∴ f1 = 56 cm

When it is equivalent to a concave mirror of focal length 10cm,

1/10 = 2/f1 + 1/fm

1/10 = 1/56 + 1/fm

solving for fm, we get,

∴ fm = 140/9 cm

The radius of curvature,

R = 2fm

R = 2 × 140/9

∴ R = 280/9 cm

The refractive index is given by,

1/f1 = (μ - 1) 1/R

1/56 = (μ - 1) × 9/280

280 / (9 × 56) + 1 = μ

∴ μ = 14/9

Therefore, the refractive index of the material of the lens is 1.555