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)
1/f = (n-1)(1/R1 + 1/R2) |