The angle (a) between the plane of the mirror and the incident beam is 7 times less than the angle (f) between

The angle (a) between the plane of the mirror and the incident beam is 7 times less than the angle (f) between the incident and reflected beams. Calculate the angle (a).

The angle between the incident and reflected rays is φ. Let us denote the angle of incidence through X, since according to the laws of optics, the angle of incidence is equal to the angle of reflection, then the angle of reflection is also equal to X. We get: X + X = φ, then X = φ / 2. It is known that the angle α between the plane of the mirror and the incident beam is 7 times less than the angle φ between the incident and reflected beams, that is, φ = 7 ∙ α. Knowing that the angle of incidence X = (7 ∙ α): 2 = 3.5 ∙ α and the angle between the plane of the mirror and the incident ray α, together make up 90 °, we get the equation: α + 3.5 ∙ α = 90 °; α = 20 °.
Answer: angle α = 20 °.