# Lens Makers Formula

The lens maker formula is utilized to create a lens with a defined focal length. A lens has two curved surfaces, but both are not exactly same. By using the lens maker’s formula you can determine the focal length of the specific lens if you know the parameters such as refractive index and radius of curvature.

$\frac{1}{f}\,&space;=\,&space;\left&space;(&space;\mu&space;-1&space;\right&space;)\left&space;(&space;\frac{1}{R_{1}}-\frac{1}{R_{2}}&space;\right&space;)$

Where,

f = Len focal length

μ = Refractive index of the material

R1 and R2 = radius of curvature of both surfaces

Example 1:

Determine the focal length of the lens with refractive index is given 2 and radius of curvature of two surfaces respectively 20cm and -35cm.

Solution:

Given

μ = 2

R1 = 30 cm

R2 = -45cm

Lens maker’s formula is

1 / f = (μ−1) (1 / R1 1 / R2 )

= 1 (1/30 + 1/45)

= 0.03 + 0.022

= 0.052

So, f = 1 / 0.052

f = 19.23 cm