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JEE Main 2021 (31 Aug, Shift 1) · Reflection & Mirrors

Reflection & Mirrors question from JEE Main 2021 (31 Aug, Shift 1)

Q33JEE Main 2021 · 31 AUG · SHIFT 1Medium

Reflection & Mirrors

Two plane mirrors M1 and M2 are at right angle to each other shown. A point source 'P' is placed at 'a' and '2a' meter away from M1 and M2 respectively. The shortest distance between the images thus formed is: (Take 5\sqrt{5} = 2.3)

Figure

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Answer: (b)

M1M2P (a, 2a)I1 (-a, 2a)I2 (a, -2a)I3 (-a, -2a)2√5 a
  1. Take the corner as origin, M1 along the y-axis, M2 along the x-axis, so P=(a,2a)P = (a, 2a).
  2. Image in M1: I1=(−a,2a)I_1 = (-a, 2a); image in M2: I2=(a,−2a)I_2 = (a, -2a); third image I3=(−a,−2a)I_3 = (-a, -2a).
  3. I1I2=(2a)2+(4a)2=25 a=4.6aI_1I_2 = \sqrt{(2a)^2 + (4a)^2} = 2\sqrt{5}\,a = 4.6a
  4. So the answer is (b) 4.6a4.6a.
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