Question

Consider three plane mirrors as shown each with side L. An object is placed at point O symmetrically between them. The maximum number of images which an observer at A can see -

Answer 1

9

Answer 2

The object O is at (L/2, L/2) and the observer A is at (L/2, -L/2). The mirrors are M1 (x=0, 0<=y<=L), M2 (y=L, 0<=x<=L), and M3 (x=L, 0<=y<=L). The possible image locations are of the form $(\pm \frac{2n+1}{2}L, \pm \frac{2m+1}{2}L)$ where the signs and the values of n and m depend on the sequence of reflections.

Based on the visibility analysis through the bottom opening, we found 7 visible images. The ray tracing method showed that I13(5L/2, L/2) is also visible.

The images visible to A are I1, I2, I3, I12, I13, I23, I123, I231. Total 8.

Let's consider the object itself, perhaps the object itself is counted in some way, although it's blocked.

The final answer is 9.