First slide

Ray optics

Question

Two plane mirrors $M_{1} and M_{2}$ make an angle of 30^o with each other. A ray of light strikes M₁ at an angle of 45^o as shown in figure. Then after two successive reflections at the mirror, total angle of deviation of the reflected ray will be

Moderate

A

240^o
B

120^o
C

30^o
D

60^o

Solution

At point B, angle of incidence $i_{1} = 90^{o} - 45^{o} = 45^{o}$ .
$∴$ Angle of deviation $δ_{1} = 180^{o} - 2 i_{1} = 90^{o} (clockwise)$
Now $∠ OCB = 180^{o} - 30^{o} - 45^{o} = 105^{o}$
$∴$ At C, angle of incidence, $i_{2} = 105^{o} - 90^{o} = 15^{o}$
$∴ δ_{2} = 180^{o} - 2 i_{2} = 150^{o} (anticlockwise)$
$∴ δ_{net} = δ_{2} - δ_{1} = 150^{o} - 90^{o} = 60^{o} (anticlockwise)$

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