Two flat rectangular mirrors are set edge to edge and placed perpendicular to a flat non-reflecting surface.A light ray that reflects from mirror 1 at angle $\theta$M1 then strikes the second mirror and reflects at $\theta$M2 such that the angle between the ray reaching mirror 1 and the ray leaving mirror 2 is 180 $\degree$.The angle between the two mirrors is:
A)0 $\degree$.
B)45 $\degree$.
C)90 $\degree$.
D)150 $\degree$.
E)235 $\degree$.

Question

Quizplus · Accepted Answer

Since the light ray reflects off the first mirror at angle F1F1F1S1F1F1F10M1 and reflects off the second mirror at angle F1F1F1S1F1F1F10M2, and since the angle between the two rays is 180F1F1F1S1F1F1F10, we know that angle F1F1F1S1F1F1F10M1 + angle F1F1F1S1F1F1F10M2 = 180F1F1F1S1F1F1F10. Since both mirrors are flat and rectangular, we know that the sum of the angles between them is 180F1F1F1S1F1F1F10, and since the light ray strikes mirror 1 perpendicularly, we know that angle F1F1F1S1F1F1F10M1 is 90F1F1F1S1F1F1F10. Therefore, angle F1F1F1S1F1F1F10M2 must be 90F1F1F1S1F1F1F10, and the angle between the two mirrors is 90F1F1F1S1F1F1F10.

Two Flat Rectangular Mirrors Are Set Edge to Edge and Placed