A light ray is incident, at an incident angle θ 1 , on the system of two plane mirrors M 1 and M 2 having an inclination angle 75 ° between them (as shown in figure). After reflecting from mirror M 1

Question

A light ray is incident, at an incident angle $θ_{1}$ , on the system of two plane mirrors $M_{1}$ and $M_{2}$ having an inclination angle $75 °$ between them (as shown in figure). After reflecting from mirror $M_{1}$ it gets reflected back by the mirror $M_{2}$ with an angle of reflection $30 °$ . The total deviation of the ray will be _____ degree.

TestHub · Accepted Answer

From the above figure, i 2 = 30 ° , Now, ∠ O B A + ∠ A B R + ∠ R B P = 180 ° ⇒ 2 ∠ O B A + 60 ° = 180 ° ⇒ ∠ O B A = 60 ° In triangle O A B , ∠ O B A + ∠ A O B + ∠ O A B = 180 ° ⇒ 60 ° + 75 ° + ∠ O A B = 180 ° ⇒ ∠ O A B = 45 ° And, ∠ O A B + ∠ B A I + ∠ I A Q = 180 ° ⇒ 2 ∠ O A B + 2 i 1 = 180 ° ⇒ i 1 = 45 ° Now the total deviation of the ray will be, δ = 360 ° - 2 i 1 + i 2 ⇒ δ = 360 ° - 2 30 ° + 45 ° δ = 210 °

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