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 =
(90−θ)
∴ 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)
∴ for the triangle
ΔRAQ
⇒4θ−180o+180o−2θ+θ=180o
⇒3θ=180o
⇒θ=60o
Hence, option
(D) is correct.