Question

Two plane mirrors touch along one edge, where they make an angle of 53.7 degrees. A beam of light is directed onto one of the mirrors at an angle of incidence of 38.2 degrees and is reflected onto the other mirror. What is the angle of reflection from the second mirror?

Answer 1

Let's sketch the problem to understand better:

Since the angle of reflection is congruent to the angle of incidence, we have r1 = i1 = 38.2°.

Now, let's calculate angle x, knowing that it is complementary to the angle r1:

`\begin{gathered} x+r1=90\\ \\ x+38.2=90\\ \\ x=90-38.2\\ \\ x=51.8° \end{gathered}`

To calculate angle y, let's add all angles in the triangle and equate the sum to 180°:

`\begin{gathered} x+y+53.7=180\\ \\ 51.8+y+53.7=180\\ \\ y+105.5=180\\ \\ y=180-105.5\\ \\ y=74.5° \end{gathered}`

Angles i2 and y are complementary, so we have:

`\begin{gathered} i2+y=90\\ \\ i2+74.5=90\\ \\ i2=90-74.5\\ \\ i2=15.5° \end{gathered}`

Since r2 and i2 are congruent, so the angle of reflection in the second mirror is 15.5°.