Question

The plane face of a planoconvex lens is silvered. The refractive index of material and radius of curvature of the curved surface of the lens are n and R respectively. This lens will behave as a concave mirror of focal length ______.

Options

• `R/n`

• `R/((n - 1))`

• nR

• `R/(2(n - 1))`

Answer 1

The plane face of a planoconvex lens is silvered. The refractive index of material and radius of curvature of the curved surface of the lens are n and R respectively. This lens will behave as a concave mirror of focal length `bbunderline(R/(2(n - 1)))`.

Explanation:

By the lens maker’s formula:

`1/f_"lens" = (n - 1)(1/R_1 - 1/R_2)`

For a plano-convex lens,

Plane side (R₁) → ∞

Curved side (R₂) → −R

`1/f_"lens" = (n - 1)(0 - 1/-R)`

= `((n - 1))/R`

Since the plane surface is silvered, it acts as a plane mirror with an infinite focal length, `f_"mirror"` → ∞.

For a silvered lens, the effective focal length F is given by,

`1/F = 2(1/f_"lens") + 1/f_"mirror"`

`1/F = 2 xx ((n - 1))/R + 0`

F = `R/(2(n - 1))`