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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 mirrors is

A
90
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B
75
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C
60
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D
45
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Solution

The correct option is C 60
Given condition is shown in the figure given below, where two plane mirrors are 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 = (90θ)

for triangle ΔORQ, (according to geometry)
θ + θ +ORQ=180o
ORQ=180o2θ ...(i)

For normal N2, angle of incidence = angle of reflection
=2θ90o ...(ii)
for the triangle ΔRAQ
4θ180o+180o2θ+θ=180o
3θ=180o
θ=60o

Hence, option (D) is correct.

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