Question

Figure shows a top view of a square room. One wall is missing, and the wall 33.7° on the right is a mirror. From point P in the center of the open side, a laser is pointed at the mirrored wall. At what angle of incidence must the light strike the right-hand wall so that, after being reflected, the light hits the left corner of the back wall?

Answer 1

Let the length of each side of the room be L. The trick is to find the image of this corner in beyond the mirror. It is simply on the other side one wall-length inside the mirror. The laser must point at this image. The laser beam will run along the hypoteneus of a right triangle with the image of the far wall as the opposite side (with length L) and the adjacent side is from the laser to the image (therefore a length 1/2L+L). The angle we are looking for is obtained by the tangent function:

tan θ = L/(1.5)(L) = 0.66667 ⇒ θ = 33.690◦