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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.

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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, 1v1−1(u)=1f1 or, 1f1=130−1(−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, 1v−1v1=1f1 or 1f)1=160−130 =30−6060×30=−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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