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Question

# The plane mirrors M1 and M2 are inclined to each other such that a ray of light incident on mirror M1 and parallel to the mirror M2 is reflected from mirror M2 parallel to the mirror M1. The angle between the two mirror is (in degrees)

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Solution

## Given condition is shown in the figure given below, where two plane mirrors inclined to each other, such that a ray of light incident on the first mirror(M1) and parallel to the second mirror (M2) is finally reflected from second mirror (M2) parallel to the first mirror. where, PQ = incident ray parallel to the mirror (M2), QR = reflected ray from the mirror (M1), RS = reflected ray from the mirror (M2) which is parallel to the (M1) and θ = angle between (M1) and (M2). According to geometry, ∠PAS=∠PQM1=θ (angle on same line) ∠AQN1 = angle of incidence = 90 - θ ∠N1QR = angle of reflection = (90−θ) therefore, for triangle ΔORQ, (according to geometry) ∠θ + ∠θ +∠ORQ=180o ∠ORQ=180o−2θ ...(i) For normal N2, angle of incidence = angle of reflection =2θ−90o ...(ii) therefore, for the trianlge ΔRAQ ⇒4θ−180o+180o−2θ+θ=180o 3θ=180o θ=60o Why this question? Note: The key to solve such questions is to apply the reflection laws at all the reflecting surfaces along with the specific condition that the question demands.

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