Question

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

a.9/14
b.14/9
c.17/9
d. none of these

Answer 1

The refractive index is n = 1 and n = 9/7 and is a contradiction hence option D is correct =.

For a spherical mirror, the focal length (f) and the radius of curvature (R) are related by the following equation:

1/f = (n - 1)/R

where n = the refractive index of the material.

Case 1 f₁ = 28 cm and R₁ is the radius of curvature for the plane surface. The equation becomes:

1/28 = (n - 1)/∞

This leads to n = 1.

Case 2 : f₂ = 10 cm and R₂ is the radius of curvature for the curved surface.

1/f₁ + 1/f₂ = 1/R

1/28 + 1/10 = 1/R₂

R₂ = 7 cm

we can apply the focal length equation:

1/10 = (n - 1)/7

n = 9/7