Question

Using the relation for refraction at a curved spherical surface, derive the expression for lens maker’s formula.

Answer 1

For refraction at a spherical surface:

`n_2/v - n_1/u = (n_2 - n_1)/R`

Apply this to both surfaces of a thin lens.

For air to lens:

`mu/v_1 - 1/u = (mu - 1)/R_1`    ...(i)

For lens to air:

`1/v - mu/v_1 = (1 - mu)/R_2`    ...(ii)

Adding equations (i) and (ii), and eliminating v₁:

`1/v - 1/u = (mu - 1) (1/R_1 - 1/R_2)`

For focal length, u = ∞, so:

`1/f = (mu - 1) (1/R_1 - 1/R_2)`

This is the lens maker’s formula.