Final answer:
The angle between the incident and reflected ray is 106° when a ray of light is incident at a glancing angle of 37° on a plane mirror, which does not match any of the provided options.
Step-by-step explanation:
The angle between the incident ray and the reflected ray can be determined using the law of reflection which states that the angle of incidence is equal to the angle of reflection. Since the incident ray makes a glancing angle of 37° with the plane mirror, this implies that the ray is 53° from the normal (90° - 37° = 53°). Therefore, the reflected ray will also make a 53° angle from the normal, or a glancing angle of 37° with the mirror. To find the angle between the incident and reflected rays, we add the two angles with respect to the normal, which results in 106° (53° + 53°). However, none of the options provided (a) 37°, (b) 53°, (c) 90°, (d) 180° directly match the calculated value of 106°.