# Lens Makers Formula

Lens maker formula is used to construct a lens with specified focal length. A lens has two curved surfaces, but both are not exactly same. If the refractive index and the radius of curvature of both the surface are known, you can determine the focal length of that particular lens by using the given lens maker’s formula,

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

Where,

f = focal length of the lens,

μ = refractive index of the material,

R1 and R2 = radius of curvature of both surfaces.

Example 1:

Determine the focal length of the lens whose refractive index and radius of curvature of each surface are 2, 20cm and -35cm respectively.

Solution:

Given parameters are,

μ = 1,

R1 = 20 cm and R2 = -35cm

Lens maker’s formula is expressed by,

1 / f = (μ−1) (1 / R1 1 / R2 )

= 1 (1/20 + 1/35)

= 0.05 + 0.028

= 0.078

So, f = 1 / 0.078

= 12.82cm

Question 2: The refractive index of a lens is 2.5, and the two curved surfaces have a radius of curvature 10cm and -12cm respectively. Determine the focal length of the lens.

Solution:

Given parameters are,

μ = 2.5,

R1 = 10cm and R2 = -12cm

Lens maker’s formula is expressed by,

1 / f = (μ−1) (1 / R1 1 / R2)

1 / f = (2.5 -1) (1/10 + 1/12)

= 0.274

So, f = 1/ 0.274

= 3.64 cm