Question

use the following information to answer the next question.
a ray of light has an incident angle of 63.0° on mirror a. this mirror is placed so that it and a second mirror, b, form an angle of 97.0°, as shown below:
image of two mirrors a and b with light rays and angles

1. the calculated value of the angle of reflection from mirror b is ______°.

97.0°
27.0°
63.0°
34.0°

Explanation:

Step1: Find angle of reflection off A

By law of reflection, angle of reflection = incident angle = $63.0^\circ$.
Find angle between reflected ray and mirror A: $90.0^\circ - 63.0^\circ = 27.0^\circ$

Step2: Find incident angle on mirror B

Use triangle angle sum ($180^\circ$) for the triangle formed by the two mirrors and the reflected ray from A:
Angle between reflected ray and mirror B = $180^\circ - 97.0^\circ - 27.0^\circ = 56.0^\circ$
Incident angle on B = $90.0^\circ - 56.0^\circ = 34.0^\circ$

Step3: Find reflection angle off B

By law of reflection, reflection angle = incident angle = $34.0^\circ$

Answer:

D. 34.0°