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An object is placed \( 30 \mathrm{cm} \) away from a convex lens of focal length \( 10 \mathrm{cm} \) and a sharp image is formed on a screen. Now a concave lens is placed in contact with the convex lens. The screen now has to be moved by \( 45 \mathrm{cm} \) to get a sharp image again. The magnitude of focal length of the concave len is (in cm)

1. 72
2. 60
3. 36
4. 20

Correct answer: 20

Solution

The convex lens alone forms an image at 15 cm on the other side. After the concave lens is added, the screen must move 45 cm farther, so the new image is at 60 cm. Using the lens formula for the combined focal length gives the concave lens focal length as 20 cm in magnitude.

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