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Q.

Two plane mirrors are separated by an angle of $' θ'$ as shown in figure. If the ray strikes mirror $M_{1}$ at angle i then the angle r at which the ray leaves mirror $M_{2}$ is

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a

r = θ - i

b

r = 2 θ

c

r = 2 θ + i

d

r = θ - 2 i

answer is B.

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Detailed Solution

According to law of reflection

x = i

$y = 90 - i$

$from Δ A B C y + θ + z = 180 °$

$z = 180 - y - θ$

$z = 180 - 90 + i - θ$

$z = 90 + i - θ$

$r = 90 - z$

$r = 90 - 90 - i + θ$

$r = θ - i$

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Two plane mirrors are separated by an angle of 'θ' as shown in figure. If the ray strikes mirror M1 at angle i then the angle r at which the ray leaves mirrorM2 is