Question

If a ray of light strikes a mirror at an angle of `24^circ` relative to horizontal, at what angle should the mirror be tilted to reflect the ray parallel to the horizontal?

Answer 1

We know that the angle between incident ray and reflected ray is twice the angle of incidence.

Let the plane mirror be placed in such a way that the incident rays which make `24^@` angle (towards left) with the horizontal ,fall on the mirror normally. So the reflected rays will retrace its path. Now if the mirror is rotated `12^@` in anticlock-wise direction, then the incident angle will be `12^@`. So reflected rays will make `24^@` angle with the incident rays and will be reflected in horizontal direction.

Again if the mirror be rotated from its initial normal position at an angle `((180-24)/2=78^@)` in clockwise direction then the incident angle will be `78^@`.In this situation the reflected rays will make angle `156^@` with the incident rays which make `24^@` angle with the horizontal.So now the reflected rays will also be horizontal in reverse direction of first situation..

Answer 2

At an angle of `76^@` relative to the sun's rays (or `76^@` relative to the earth measuring on the side opposite the approach of the sun's rays)

Explanation:

`2x^@+24^@=180^@color(white)("xxx")rarrcolor(white)("xxx")x^@=78^@`