Question 34.2: The Double-Reflected Light Ray Two mirrors make an angle of ...
The Double-Reflected Light Ray
Two mirrors make an angle of 120° with each other as illustrated in Figure 34.7a. A ray is incident on mirror M_1 at an angle of 65° to the normal. Find the direction of the ray after it is reflected from mirror M_2.
Conceptualize Figure 34.7a helps conceptualize this situation. The incoming ray reflects from the first mirror, and the reflected ray is directed toward the second mirror. Therefore, there is a second reflection from the second mirror.
Categorize Because the interactions with both mirrors are simple reflections, we apply the wave under reflection model and some geometry.
Analyze From the law of reflection, the first reflected ray makes an angle of 65° with the normal.
Find the angle the first reflected ray makes with the horizontal:
\delta=90^{\circ}-65^{\circ}=25^{\circ}From the triangle made by the first reflected ray and the two mirrors, find the angle the reflected ray makes with M_2 :
\gamma=180^{\circ}-25^{\circ}-120^{\circ}=35^{\circ}Find the angle the first reflected ray makes with the normal to M_2:
\theta_{M_2}=90^{\circ}-35^{\circ}=55^{\circ}From the law of reflection, find the angle the second reflected ray makes with the normal to M_2:
\theta_{M_2}^{\prime}=\theta_{M_2}=55^{\circ}Finalize Let’s explore variations in the angle between the mirrors as follows.