## Question

The radius of curvature of both the surfaces of a double convex lens is *R*. The refractive index of the material of the lens is 1.5. When a point-source of light is placed on the principal axis of the lens at a distance of 20 cm in-front of the one surface of the lens, then rays emerge from the other surface normally. Determine the radius of curvature *R* of each surface of the lens.

### Solution

40 cm

A point-source *O* is placed at a distance of 20 cm in front of the lens. The rays emerging normally from the second surface of the lens will appear to come from the centre of curvature *C*_{2} of the second surface, as shown. Thus, *C*_{2} is virtual image of the source *O*. Now, for the lens, we have

*u* = –20cm and *v* = –*R*. The lens formula is

Putting the above values of *u* and *v*. we have

or *R* = **40 cm**.

#### SIMILAR QUESTIONS

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