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JEE Main 2018 (15 Apr, Shift 1) · Reflection & Mirrors

Reflection & Mirrors question from JEE Main 2018 (15 Apr, Shift 1)

Q45JEE Main 2018 · 15 APR · SHIFT 1Difficult

Reflection & Mirrors

A particle is oscillating on the XX-axis with an amplitude 2 cm2\text{ cm} about the point x0=10 cm,x_0 = 10\text{ cm}, with a frequency ω\omega. A concave mirror of focal length 5 cm5\text{ cm} is placed at the origin (see figure).

Figure

Identify the correct statements.

(A) The image executes periodic motion.

(B) The image executes non-periodic motion.

(C) The turning points of the image are asymmetric w.r.t. the image of the point at x=10 cmx = 10\text{ cm}. (D) The distance between the turning points of the oscillation of the image is 10021 cm.\frac{100}{21}\text{ cm.}

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Answer: (b)

  1. f=−5 cmf = -5\text{ cm}; object moves between u=−8u = -8 and u=−12u = -12 cm periodically, so the image is also periodic: (A) true, (B) false.
  2. v=ufu−fv = \frac{uf}{u - f}: u=−8⇒v=−403=−13.33u = -8 \Rightarrow v = -\frac{40}{3} = -13.33; u=−10⇒v=−10u = -10 \Rightarrow v = -10; u=−12⇒v=−607=−8.57u = -12 \Rightarrow v = -\frac{60}{7} = -8.57 cm
  3. Turning points are 3.33 cm and 1.43 cm from the image of x=10x = 10 cm, so they are asymmetric: (C) true.
  4. Distance =403−607=10021 cm= \frac{40}{3} - \frac{60}{7} = \frac{100}{21}\text{ cm}: (D) true.
  5. So the answer is (b) (A), (C), (D).
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