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A ray of light travelling in the directi...

A ray of light travelling in the direction `(1)/(2)``(hati,+sqrt3hatj)` is incident on a plane mirror. After reflection, it travels along the direction `(1)/(2)(hati-sqrt3hatj)` . The angle of incidence is

A

`30^(@)`

B

`45^(@)`

C

`60^(@)`

D

`75^(@)`

Text Solution

Verified by Experts

The correct Answer is:
A

Let `theta` be angle between the given rays,
`:. cos theta = (((hati+sqrt(3)hatj)/(2)).((hati-sqrt(3)hatj)/(2)))/(|(hati+sqrt(3)hatj)/(2)||(hati-sqrt(3)j)/(2)|) = ((1.3)/(4))/(1) = -1/2`
`theta = cos^(-1)(-1/2) = 120^(@)`
Angle of incidence, `i = (180^(@) - theta)/(2)= (180^(@) - 120^(@))/(2) = 30^(@)`
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