Question

Write the basic assumptions used in the derivation of lens – maker’s formula and hence derive this expression.

Answer 1

Basic assumptions used in deviation of lens maker formula are as follow:

1)The lens should be thin so that distances measured from its surface may be taken equal to those measured from optical centre .

2)Object should be a point object.

3)Aperture of lens should be small.

4)All rays are paraxial that is make very small angles with lens faces and principal axis.

Let refractive index of lens =u2

Then refractive index of medium =u1

u2>u1 object distance=u

From one surface of lens image distance =v1 and radius of curvature of surface =R1

So relation is u2/v1-u1/u=u2-u1/R1..........(1)

As it suffers refraction so u=v from other surface whose radius of curvature=R2

u1/v-u2/v1=u1-u2/R2........(2)

Adding equations (1) and (2) we have

u1/v-u1/u=(u2-u1)[1/R1-1/R2]

1/v-1/u=[u2-u1/u1][1/R1-1/R2]........(3)

If object at infinity then image at focus that is v=f

i/f=[u2-u1/u1][1/R1-1/R2]....(4) this is lens maker's formula

u1=1 as air so we have

1/f=(u2-1)[1/R1-1/R2]

From equation (3) and (4) we have

1/f=1/v-1/u