An object AB is placed 15 cm to the left of a convex lens P of focal length 10 cm. A second convex lens Q of focal length 15 cm is placed 15 cm to the right of lens P. Which statement correctly describes the final image formed by the two-lens system?
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Question

An object AB is placed 15 cm to the left of a convex lens P of focal length 10 cm. A second convex lens Q of focal length 15 cm is placed 15 cm to the right of lens P. Which statement correctly describes the final image formed by the two-lens system?

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G1 Physics · Accepted Answer

For lens P, use 1 ÷ f = 1 ÷ v - 1 ÷ u. Here, f(P) = +10 cm, u(P) = -15 cm. Therefore, 1 ÷ 10 = 1 ÷ v(P)+1 ÷ 15, so v(P) = +30 cm. Lens Q is 15 cm to the right of P. Thus the image formed by P lies 15 cm to the right of Q and acts as a virtual object for Q: u(Q) = +15 cm. For Q, 1 ÷ 15 = 1 ÷ v(Q) - 1 ÷ 15. Therefore, 1 ÷ v(Q) = 2 ÷ 15, so v(Q) = +7.5 cm. The magnification of P is m₁ = 30 ÷ (-15) = -2. For Q, m₂ = 7.5 ÷ 15 = 1 ÷ 2. Hence, m(total) = m₁m₂ = -1. The final image is real, inverted, a…