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JEE Main 2016 (9 Apr, Shift 1) · Combination of Lenses

Combination of Lenses question from JEE Main 2016 (9 Apr, Shift 1)

Q70JEE Main 2016 · 9 APR · SHIFT 1Difficult

Combination of Lenses

A convex lens, of focal length 30 cm, a concave lens of focal length 120 cm, and aplane mirror are arranged as shown. For an object kept at a distance of 60 cm from the convex lens, the final image, formed by the combination, is a real image, at a distance of:

Figure

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Answer: (a)

  1. Convex lens: u=2f=60⇒v=60 cmu = 2f = 60 \Rightarrow v = 60\text{ cm}, i.e. 40 cm beyond the concave lens.
  2. Concave lens (virtual object u=+40u = +40): 1v=−1120+140=160⇒v=60 cm\frac{1}{v} = -\frac{1}{120} + \frac{1}{40} = \frac{1}{60} \Rightarrow v = 60\text{ cm}, i.e. 80 cm from the convex lens, 10 cm behind the mirror.
  3. Plane mirror: rays now converge to a point 10 cm in front of it, a real image at 70−10=60 cm70 - 10 = 60\text{ cm} from the convex lens.
  4. So the answer is (a) 60 cm from the convex lens.
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