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JEE Main 2022 (26 Jun, Shift 1) · Reflection & Mirrors

Reflection & Mirrors question from JEE Main 2022 (26 Jun, Shift 1)

Q28JEE Main 2022 · 26 JUN · SHIFT 1Medium

Reflection & Mirrors

A light ray is incident, at an incident angle θ\theta1, on the system of two plane mirrors M1 and M2 having an inclination angle 75∘^\circ between them (as shown in figure). After reflecting from mirror M1 it gets reflected back by the mirror M2 with an angle of reflection 30∘^\circ. The total deviation of the ray will be _____________ degree.

Figure

Numerical answer type. Work it out, then open the answer.

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Answer: 210

M1M275°45°60°60°incident
  1. At M2 the angle of reflection is 30∘30^\circ, so the ray meets M2 at 60∘60^\circ to the surface; deviation at M2 =180∘−2(30∘)=120∘= 180^\circ - 2(30^\circ) = 120^\circ.
  2. Triangle of the mirrors and the ray: angle with M1 =180∘−75∘−60∘=45∘= 180^\circ - 75^\circ - 60^\circ = 45^\circ, so θ1=45∘\theta_1 = 45^\circ.
  3. Deviation at M1 =180∘−2(45∘)=90∘= 180^\circ - 2(45^\circ) = 90^\circ
  4. Total deviation =90∘+120∘=210∘= 90^\circ + 120^\circ = 210^\circ
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