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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

Refer to the figure . Let angle between the directions of incident ray and reflected ray be `theta` .
Here, `cos theta =(1)/(2) (hati+sqrt3hatj). (1)/(2) (hati-sqrt3hatj)`
`rArr cos theta = -(1)/(2)`
`rArr theta =120^(@)`
Let `alpha` be the angle of incidence, then we can write the following:
`2alpha+theta=180^(@) rArr 2 alpha +120 =180 rArr alpha =30^(@)`
Hence option (a) is correct .
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