Question

A thin lens is made of glass that has refractive index n = 1.50. The lens is surrounded by air. The left-hand spherical surface of the lens is concave with radius of curvature R and the right-hand side is flat, so the lens is thinner in the middle than at its edges. An object is placed 12.0 cm to the left of the center of the lens.

What is the value of R if the image formed by the lens is 7.50 cm to the left of the center of the lens?

Answer 1

See the diagram :

u = object distance = 12 cm

v = image diatnce = 7.5 cm

n = refractive index = 1.5

R = radius of curvature = to be calculated.

I will use cartesian sign convention, in which measurement is taken positive in the direction of incident light, and negative opposite to the direction of incident light.

All measurements are taken from center of lens.

Using lens maker formula :

----- (i)

Now, using lens's formula :

=> R = 10cm

The radius of curvature of the curved surface is -10 cm (according to sign convention).