Two plane mirrors are inclined at angle \(45^{\circ}\) one to another. A ray of light has incident angle \(20^{\circ}\) at the surface of the first mirror. The reflected ray is then incident on the second mirror. Calculate the angle of reflection at the second mirror.
Explanation
Since angle on a straight line equals \(180^{\circ}\) and \(g^{\prime}=g^{\prime}\), \(2 g ^{\prime}=180-\left(i_{1}+r_{1}\right)\)
\(=180^{\circ}-\left(20^{\circ}+20^{\circ}\right)=140^{\circ}\),
\(g^{\prime}=70^{\circ}\)
see also that a triangle is formed with, \(g^{\prime}\) and \(g^{\prime \prime}\), the sum of which equals \(180^{\circ}\)
\(45^{\circ}+g^{\prime}+g^{\prime \prime}=180^{\circ}\).
\(45^{\circ}+70+g^{\prime \prime}=180^{\circ}\)
\(g^{\prime \prime}=180-115^{\circ}=65^{\circ}\) also for the second plane mirror
\(g^{\prime \prime}+i_{2}+r_{2}+g^{n}=180\) (sum of angles on a straight line)
\(2 g^{\prime \prime}+2 r_{2}=180^{\circ}\left(i_{2}=r_{2}\right)\)
\(2 \times 65+2 r_{2}=180^{\circ}\)
\(2 r_{2}=180-130, r_{2}=50 / 2=25^{\circ}\)
