The sunbeam is directed horizontally. How should a flat mirror be positioned so that after reflection the beam goes vertically?

According to the law of reflection, the angle of incidence of a sunbeam is equal to the angle of reflection of sunlight:
α = β.

If you change the angle of incidence of the light beam on the mirror by a certain value, then the angle of reflection will change by an equal value. And the total change in the angles of incidence and reflection will give twice the change in the angle of incidence:

Δa = 2α. (one)

Based on this, it is easy to guess that the mirror must be positioned so that the total change in the angle is 90 °.

Substitute this value into formula 1 and get:

90 = 2α ->

α = 90/2 = 45 – the angle of the mirror in relation to the sunlight, on which it should be placed in order to change the direction of the beam from horizontal to vertical.

Answer: 45.