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A parallel beam of light falls on a converging lens of focal length f1 = 20 cm. A diverging lens of focal length f2 = -20 cm is placed coaxially at distance L behind the converging lens. After passing through both lenses, the light converges at point A which is 5 cm behind the diverging lens. The positions of the two lenses are then interchanged. Which of the following statements are correct?

1. The value of L is 16 cm.
2. The value of L is 80/3 cm.
3. Point A shifts by 40 cm after the lenses are interchanged.
4. Point A shifts by 125/3 cm after the lenses are interchanged.

Correct answer: The value of L is 16 cm.

Solution

With the converging lens first, the parallel beam focuses at 20 cm; the diverging lens intercepts it at distance L and re-focuses 5 cm behind itself. Setting up the lens equation gives L = 16 cm. After interchanging, the diverging lens acts first on the parallel beam, creating a virtual image that the converging lens then focuses at 45 cm behind it — a shift of 40 cm from the original 5 cm position (measured from the second lens). Both statements A and C are correct.

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