Question

Derive lens maker formula for convex lens ​

Answer 1

Answer:

in case of convex lens focal length is positive.

Answer 2

Assumptions;

The following assumptions are taken for the derivation of lens maker formula.

• Let us consider the thin lens shown in the image above with 2 refracting surfaces having the radii of curvatures R1 and R2, respectively.
• Let the refractive indices of the surrounding medium and the lens material be n1 and n2, respectively.

Derivation;

The complete derivation of lens maker formula is described below. Using the formula for refraction at a single spherical surface we can say that

For the first surface,

$\frac{n_{2} }{v_{1}} - \frac{n_{1} }{u} = \frac{n_{2} - n_{1}}{R_{1} } \: \: \: \: ... (1)$

For the second surface,

$\frac{n_{1} }{v} - \frac{n_{2} }{v_{1}} = \frac{n_{1} - n_{2}}{R_{2} } \: \: \: \: ... (2)$

Now adding equation (1) and (2),

$\frac{n_{1} }{v} - \frac{n_{1} }{u} = ({n_{2} - n_{1}})( \frac{1}{R_{1}} - \frac{1}{R_{2}}) \\ = > \frac{1}{v} - \frac{1}{u} = ( \frac{n_{2}}{n_{1} } - 1)( \frac{1}{R_{1}} - \frac{1}{R_{2}})$

When u = ∞ and v = f

$\frac{1}{f} = ( \frac{n_{2}}{n_{1} } - 1)( \frac{1}{R_{1}} - \frac{1}{R_{2}})$

But Also,

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Therefore, we can say that,

$\frac{1}{f} = ( μ - 1)( \frac{1}{R_{1}} - \frac{1}{R_{2}})$

Where μ is the refractive index of the material.

Where μ is the refractive index of the material.This is the lens maker formula derivation. Check the limitations of the lens maker’s formula to understand the lens maker formula derivation is a better way.