# Numerical based on Lens Makers’ equation – solved

In this post, we will solve numerical problems based on Lens Makers’ Equation.

Here is our post on the equation used here which you can read: Lens Makers’ equation.

## Numerical based on Lens Makers’ equation – with solution

A dense glass double convex lens [n =2] designed to reduce spherical aberration has |R1|:|R2|=1:5. If a point object is kept 15 cm in front of this lens, it produces its real image at 7.5 cm. Determine R1 and R2.

**Solution: **

u = – 15 cm, v = + 7.5 cm (the real image is on the opposite side).

1/f = 1/v -1/u

=>1/f = 1/7.5 -1/[-15]

so, f = +5 cm

The lens is double convex. Hence, R1 is positive and R2 is negative. Also, |R2| = 5|R1| and n = 2.

**Answer: R1 = 6 cm and R2 = 30 cm**