The sun’s rays hit the earth at an angle of 36 degrees to its surface. At what angle to the horizon should

The sun’s rays hit the earth at an angle of 36 degrees to its surface. At what angle to the horizon should a flat mirror be positioned in order to direct the rays reflected from it horizontally from the Sun?

Let the sun’s rays fall on the earth at an angle ∠ AOC = 36 ° to its surface AB. We place the flat mirror KO under ∠ AOK = β to the earth’s surface so that the beam OB reflected from it is directed horizontally from the Sun. Let us draw a perpendicular TO ⊥ KO through the point of incidence of the beam on the mirror. According to the law of optics, the angle of incidence of the beam is equal to the angle of reflection: ∠ СOT = ∠ TOВ. On the other hand, if we continue the straight line along the mirror KO beyond the point O, we get a ray OM such that ∠ AOK = ∠ ВOM = β – as vertical angles; ∠ СOK = ∠ MOВ = β – as additional for ∠ СOT = ∠ TOВ. Then ∠ СOK = ∠ AOK = β, β = ∠ AOC: 2 = 36 °: 2 = 18 °.

Answer: a flat mirror should be placed at an angle of 18 ° to the horizon.