Lens-Formula

Description:

To study lens formula, we will use a convex lens with object AB placed on the principle axis.

We will consider two rays, one ray that is parallel to principle axis and after refraction will pass through the focus. Second ray is directed towards the optical center and it will pass un-deviated.

These two rays intersect at point A’ and this is the image of point A. Point B is on the principle axis so the image of point B will also be on the principle axis.

As we can observe that the object is perpendicular to principle axis, hence the image will also be perpendicular to principle axis. So when we draw a perpendicular from point A’ to principle axis we get the location of image of point B which is denoted by B’.

From figure −

In similar ΔABO and ΔA′B′O

AB/A′B′ = BO/OB′ ......(1)

In similar ΔPOF and ΔFB′A′

PO/OF = A′B′/FB′

From figure we can easily observe that PO = AB

∴ AB/OF = A′B′/FB′

∴ AB/A′B′ = OF/FB′ ........(2)

By comparing equation 1 and equation 2, we get −

BO/OB′ = OF/FB′

∴ BO/OB′ = OF/OB′ - OF

Substituting values as optical distances −

-u/+v = +f/v - f

∴ -uv + uf = fv

Dividing both sides by u v f, we get −

-1/f + 1/v = 1/u

1/v = 1/u + 1/f

It can also be written as −

1/f = 1/v - 1/u

This equation is known as lens formula.