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Question

A point object is placed at a distance of 15 cm from a convex lens. The image is formed on the other side at a distance of 30 cm from the lens. When a concave lens is placed in contact with the convex lens, the image shifts away further by 30 cm. Calculate the focal lengths of the two lenses.


Solution

Let u = object distance from convex lens

= -15 cm

v1= image distance from convex lens

= 30 cm

f1= focal length of convex lens.

Now, 1v11(u)=1f1

or, 1f1=1301(15)=130+115

or, f1=30×1530+15=45045

= 10 cm

Again, let v = image (final) distance from concave lens = + (30 + 30) = + 60 cm

v1= object distance from concave lens

= + 30 cm

f2= focal length of concave lens

Now, 1v1v1=1f1

or 1f)1=160130

=306060×30=3060×30

or,  f2=60 cm

So, the focal length of convex lens is 10 cm and that of concave lens is 60 cm.

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