Lens Maker Formula

Lens maker formula is an expression that shows relation between the refractive index, the focal length and the radii of curvatures of the lens.

1f = (n−1)(1R1 + 1R2)

where,

f = focal length of the lens

n = refractive index of the lens

R₁ ,R₂ = radii of curvatures of the lens

Assumptions:

1. The lens is thin

2. deviation produced by the thin lens is similar to that of a small angle prism

3. angle made by incident ray and refracted ray with principle axis is small

:

from fig:

In  ΔXOF,

tanδ = OX/OF

or, tanδ = h/f

for small angle tanδ ≈ δ

.˙. δ = h/f.............:1

we know,

δ = A(n-1)............:2

from equations 1 and 2

h/f =A(n-1)............:3

from geometry,

angle MXG = A

or, A = a+a'

or, A = h/R₁ + h/R₂

or A =h(1/R₁ + 1/R₂).............:4

now, from equation 3

or, h/f = h(n-1)(1/R₁ + 1/R₂)