A light ray is incident on a plane mirror, which after getting reflected strikes another plane mirror, as shown in figure. The angle between the two mirrors is 60°. Find the angle q shown in figure. Correct answer is '60'. Can you explain this answer?

Question

A light ray is incident on a plane mirror, which after getting reflected strikes another plane mirror, as shown in figure. The angle between the two mirrors is 60&deg;. Find the angle q shown in figure.        Correct answer is '60'. Can you explain this answer?

Answer

Answer

Figure shows two plane mirrors kept at angle 60°. A light ray incidents at A making an angle of incidence α,
reflected and again incidents at B making an angle β and getting reflected .
Reflected ray from B makes angle θ with the initial incident ray.
At reflection point A, as shown in figure, we have α+x = 90° ..............(1)
At reflection point B, as shown in figure, we have β+y = 90° ..............(2)
By adding (1) and (2), after substituting x+y = 120°, we get, α+β = 60° ...............(3)
From ΔABC, we have, 2α + 2β + θ = 180° ...................(4)
Hence By using eqn.(3), we get , θ = 180 - 120 = 60°

Answer

Figure shows two plane mirrors kept at angle 60°. A light ray incidents at A making an angle of incidence α,
reflected and again incidents at B making an angle β and getting reflected .
Reflected ray from B makes angle θ with the initial incident ray.
At reflection point A, as shown in figure, we have α+x = 90° ..............(1)
At reflection point B, as shown in figure, we have β+y = 90° ..............(2)
By adding (1) and (2), after substituting x+y = 120°, we get, α+β = 60° ...............(3)
From ΔABC, we have, 2α + 2β + θ = 180° ...................(4)
Hence By using eqn.(3), we get , θ = 180 - 120 = 60°

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