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

**(a)** Focal
length of the convex lens, *f*
= 20 cm

Image
distance = *v*

According to the lens formula, we have the relation:

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

**(b)** Focal
length of the concave lens, *f*
= −16 cm

Image
distance = *v*

According to the lens formula, we have the relation:

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

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