Let x be the distance from the light to the wall on which the mirror is mounted. Then the distance from the person to the wall is 5x. Also let y be the component of distance parallel to the wall from the light to the point on the mirror that the light reaches before hitting the person. The light bulb is therefore be located at (x, y) with respect to this point and the person at (5x, -5y).
and reflects from
the mirror to the person. It also travels directly to the
person without reflecting off the mirror. The total distance
traveled by the light in the first case is twice the distance
traveled by the light in the second case. Find the value of
the angle &.