A ray of light in incident along a vector `hati + hatj - hatk` on a plane mirror lying in y-z plane. The unit vector along the reflected ray can be

Options

A. `(hati + hatj -hatk)/(sqrt(3))`
B. `(hati - hatj +hatk)/(sqrt(3))`
C. `(-hati + hatj -hatk)/(sqrt(3))`
D. `(3hati + hatj -hatk)/(sqrt(3))`

Answer

C, D

Explanation

According to law of reflection `hatr= hate -2(hate.hatn)hatn "Here" hate= (hati + hatj -hatk)/(sqrt(3)), hatn =pmhati`
so `hate.hatn = (1)/(sqrt(3)) implies hatr = (hati + hatj - hatk)/(sqrt(3))pm (2hati)/(sqrt(3)) = (3hati + hatj - hatk)/(sqrt(3)) "or" (-hati + hatj -hatk)/(sqrt(3))`