Two flat rectangular mirrors are set edge to edge and placed perpendicular to a flat nonreflecting surface. A light ray that reflects from mirror 1 at angle θM₁ then strikes the second mirror and reflects at θM₂ such that the angle between the ray reaching mirror 1 and the ray leaving mirror 2 is 180°. The angle between the two mirrors is A) 0°. B) 45°. C) 90°. D) 150°. E) 235°.

Question

Quizplus · Accepted Answer

When the light ray reflects off the first mirror, it follows the law of reflection, which states that the angle of incidence is equal to the angle of reflection. Therefore, the angle of reflection off the first mirror is also θM₁. When the light ray reflects off the second mirror, it follows the same law of reflection. The angle of incidence is equal to the angle of reflection, so the angle of reflection off the second mirror is also θM₂. Since the two mirrors are placed edge to edge, the angle between them is equal to the sum of the two angles of reflection. Thus, the angle between the two mirrors is θM₁ + θM₂. Since the angle between the ray reaching mirror 1 and the ray leaving mirror 2 is 180°, we know that the sum of the angles of reflection is 180°. Thus, θM₁ + θM₂ = 180°. Therefore, the angle between the two mirrors is 90°, which is choice C.

Two Flat Rectangular Mirrors Are Set Edge to Edge and Placed