Question

A beam of light converges at a point P. Now a lens is placed in the path of the convergent beam 12 cm from P. At what point does the beam converge if the lens is (a) a convex lens of focal length 20 cm and (b) a concave lens of focal length 16 cm?

Answer 1

As a lens is placed in the path of the convengent beam, the point P would lie on the right of the lens and acts as the virtual object.

(a) For convex lens f = 20 cm, u = 12 cm, v = ?

1/v - 1/u = 1/f ⇒ 1/v = 1/f + 1/v = 1/20 + 1/12 = (3 + 5)/60 = 8/60

∴ v = 60/80 = 7.5cm.

The image formed is real, at 7.5 cm from the lens on its right side.

(b) For concave lens f = – 16 cm, u = 12 cm, v = ?

1/v = 1/u + 1/f = 1/12 + 1/-16 = 1/12 - 1/16 = (4 - 3)/48 = 1/48

∴ v = 48 cm

Image is real, and at 48 cm from the lens on the right side.