Question

Derive Len's maker's formula.​

Answer 1

$\huge\rm\underline\purple{Answer}$

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,

(n2/v1) - (n1/u) = (n2-n1)/R1 .... (1)

or the second surface,

(n1/v) - (n2/v1) = (n1-n2)/R2 .... (2)

Now adding equation (1) and (2),

(n1/v) - (n1/u) = (n2 - n1) [(1/R1) - (1/R2)]

(1/v) - (1/u) = (n2/n1 - 1) [(1/R1) - (1/R2)]

When u = ∞ and v = f

1/f = ((n2/n1) - 1)[(1/R1) - (1/R2)]

But also,

(1/v) - (1/u) = 1/f

therefore, we can say that,

1/f = ( μ -1) [(1/R1) - (1/R2)]

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.

#NAWABZAADI