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Prove that w hen a mirror rotates through an angle θ a beam of light reflected from it will rotate through an angle of 2θ.


Prove that  when a mirror rotates through an angle θ a beam of light reflected from it will rotate through an angle of 2θ. 


Grade:upto college level

1 Answers

Vasantha Kumari
askIITians Faculty 38 Points
8 years ago

Consider a ray of light incident on a plane mirror at angle i and we assume it is fixed. Now, we know that the angle of reflection r is equal to i. This means the angle between these two rays is 2i.

But when we rotate the angle i further through q and now the angle of incidence will become i+q and the angle between the two becomes 2i+2q. This means the ray reflected also gets reflected twice.

Thus, on rotating a mirror through an angle, the reflected beam rotates through double the angle of rotation given to the mirror.

181-2476_angle.JPG

Regards,

Vasantha,

AskIITian Faculty,MSc, B.Ed (St. Marys College, Chennai)

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