Answer to Question #316172 in Geometry for Jrs

Question

There are two hinged vertical mirrors with an angle of

140 °. A horizontal light beam falls on one of these

mirrors at a certain angle and is then reflected from

both mirrors. What is the acute angle between the

beam incident on the first mirror and the beam

reflected from the second mirror?

Answer 1

As indicated in the figure,If i be the angle of incidence, r be the angle of reflection,δ=π−(π−2i−2r)Hence, δ=2i+2rAlso, using the sum of angles of a triangle, i+r−θ=0Thus, δ=2θWhich means, that the deviation is independent of either the angle of incidence and also the angle of relection. It only depends on the angle between the mirrors