Question

Derive lens maker formula. step by step.

please it's urgent. ​

Answer 1

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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,

Derivation Of Lens Maker Formula

For the second surface,

Derivation Of Lens Maker Formula

Now adding equation (1) and (2),

Derivation Of Lens Maker Formula

When u = ∞ and v = f

Derivation Of Lens Maker Formula

But also,

Derivation Of Lens Maker Formula

Therefore we can say that,

Derivation Of Lens Maker Formula

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