Question

derivation of lens formula

Answer 1

Derivation of Lens Formula for concave lens:

Let AB represent an object placed at right angles to the principal axis at a distance greater than the focal length f of the convex lens. The image A1B1 is formed between O and F1 on the same side as the object is kept and the image is erect and virtual.

 



 

OF1 = Focal length = f

OA = Object distance = u

OA1 = Image distance = v







Answer 2

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

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.