Question

explain lens maker formula

Answer 1

Focal length of a lens depends upon radii of curvatures of two surfaces and refractive index of the lensmaterial. Lens maker's formula is used by lens manufacturers for making lenses of desired focal lengths.
For refraction at surface-1 −

When ray moves from rarer to denser medium, we have −

μ2v - μ1u = μ2 - μ1R

From figure, we get −

v = OI′ and u = OP and R = OC1

Putting values −

μ2+OI′ - μ1-OP = μ2 - μ1-OC1

∴ μ2+OI′ + μ1OP = μ2 - μ1OC1...........(1)

For refraction at surface-2 −

When ray moves from denser to rarer medium, we have −

μ1v - μ2u = μ1 - μ2R

From figure, we get −

v = OI and u = OI′ and R = OC2

Putting values −

μ2+OI - μ1+OI′ = μ1 - μ2-OC2

∴ μ2OI - μ1OI′ = μ2 - μ1OC2.......(2)

Adding equation 1 and equation 2, we get −

μ1OI + μ1OP = (μ2 - μ1)(1OC1 + 1OC2)

Now, from figure considering values for lens −

OI = +v and OP = -u

Putting values for lens −

μ1v + μ1-u = (μ2 - μ1)(1R1 + 1-R2)

μ1(1v - 1u) = (μ2 - μ1)(1R1 - 1R2)

Therefore,

1f = (μ2μ1 - 1)(1R1 - 1R2)

Writing in terms of power −

P = (μ21 - 1)(1R1 - 1R2)

Answer 2

Using the positive optical sign convention, the lens maker's formula states
1/f=(n-1)(1/R1-1/R2)



Using the positive optical sign convention, the lens maker's formula states


where f is the focal length, n is the index of refraction, and R1 and R2 are the radii of curvature of the two sides of the lens.

hope it helped......☺️