What is the derivation of lens maker formula?

Answer 1

Derivation of Lens-maker's Formula:Derivation of Lens-Maker's formula:

As shown in figure the centre of the lens is denoted as C and the principal axis is X'X. The R1 and R2 are the radii of the curvature of the surfaces of lens and the poles are P1 and P2. The variable t represents the thickness of the lens which has the small value. The object in principal axis is O. The distance between the point object and the pole P1 is u. The image of point object O is refracted at I which has the distance v' from the pole P1.

Based on the refraction formula of the spherical surface,

- =

In second surface the virtual object is denoted as I' after completion of refraction the final complete image should be created at I. The distance between the final object I and the pole is v. The distance between the virtual object I' and the pole P2 is (v'-t).

If there is refraction at second medium then the ray is moving from the second medium to first medium.

Derivation of Lens-maker's Formula:Refraction formula,

- = -----------------------------(1)

Here the value of t is negligible because it has very small value. Therefore the equation becomes

- = - --------------------------------(2)

By adding the equations (1) and (2) we get,

- =

=

=

Where the refractive index of the second medium is denoted as which is related to the first medium.

When the object is at infinity, the image should be created at second focus. That is u=∞, v=f2=f.

=

Therefore refraction formula for thin lens:

=

Which is known as Lens-Maker's formula.

Consider the air is the first medium and n be the refractive index of the material. In this

Now the derivation of Lens-Maker's formula is,

= (n-1)