Two vertical plane mirrors are inclined at an angle of $6 0^{0}$ with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

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Answer 1

$F r o m t h e f i g u r e a + b = 9 0^{0} \Rightarrow b = 9 0^{0} - a N o w, b + 60 + c = 180 \Rightarrow c = 180 - 60 - b = 180 - (90 - a) = 30 + a N o w, d + c = 90 d = 90 - c = 90 - (30 + a) = 60 - a T h u s, i n t r i a n g l e P Q R ∠ Q = 2 a ∠ R = 2 d = 2 (60 - a) = 120 - 2 a s o, a n g l e ∠ Q P T i s = ∠ Q + ∠ R = 120 N o w, a n g l e o f d e v i a t i o n = r e f l e x ∠ Q P T = 360 - 120 = 24 0^{\circ} H e n c e, t h e o p t i o n D i s t h e c o r r e c t a n s w e r .$

Answer 2

F r o m t h e f i g u r e a + b = 9 0^{0} \Rightarrow b = 9 0^{0} - a N o w, b + 60 + c = 180 \Rightarrow c = 180 - 60 - b = 180 - (90 - a) = 30 + a N o w, d + c = 90 d = 90 - c = 90 - (30 + a) = 60 - a T h u s, i n t r i a n g l e P Q R ∠ Q = 2 a ∠ R = 2 d = 2 (60 - a) = 120 - 2 a s o, a n g l e ∠ Q P T i s = ∠ Q + ∠ R = 120 N o w, a n g l e o f d e v i a t i o n = r e f l e x ∠ Q P T = 360 - 120 = 24 0^{\circ} H e n c e, t h e o p t i o n D i s t h e c o r r e c t a n s w e r .