A ray of light travelling in the direction `(1)/(2)(hat(i)+sqrt(3)hat(j))` is incident on a plane mirror. After reflection, it travels along the direction `(1)/(2)(hat(i)-sqrt(3)hat(j))` . The anglel of incidence is

Options

A. `30^(@)`
B. `45^(@)`
C. `60^(@)`
D. `75^(@)`

Answer

A

Explanation

Here, `vec(A) = (1)/(2)(hat(i) + sqrt(3) hat(j))`
and `vec(B) = (1)/(2)(hat(i) - sqrt(3) hat(j))`
`:. A = B = sqrt(1^(2) + (sqrt(3))^(2)) = 2 and vec(A).vec(B) = 2`
`cos theta = (vec(A).vec(B))/(A B) = (-2)/(2 xx 2) = -(1)/(2)`
`theta = 120^(@)`, Fig.

Angle of incidence,
`i = (180^(@) - theta)/(2) = (180^(@) - 120^(@))/(2) = 30^(@)`