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?

In the given situation, the object is virtual and the image formed is real.

Object distance, u = +12 cm

Ans (a).

Focal length of the convex lens, f = 20 cm

Image distance = v

According to the lens formula, we have the relation:

1/v – 1/u = 1/f

1/v -1/12 = 1/20

1/v = 1/20 + 1/12 = (3+5)/60 = 8/60

Therefore , v = 60/8 = 7.5 cm

Hence, the image is formed 7.5 cm away from the lens, toward its right.

Ans (b).

Focal length of the concave lens, f = -16 cm Image distance = v

According to the lens formula, we have the relation:

1/v – 1/u = 1/f

1/v – 1/12 = 1/16

=> 1/v = 1/(-16) + 1/12 = -1/16 + 1/12

=>1/v = (-3+ 4)/48 =1/48

v = 48 cm

Hence, the image is formed 48 cm away from the lens, toward its right.