Question

Figure 34-27 is an overhead view of a mirror maze based on floor sections that are equilateral triangles. Every wall within the maze is mirrored. If you stand at entrance $\mathit{x}$, (a) which of the maze monsters $\mathit{a}$, $\mathit{b}$, and $\mathit{c}$hiding in the maze can you see along the virtual hallways extending from entrance $\mathit{x}$; (b) how many times does each visible monster appear in a hallway; and (c) what is at the far end of a hallway?

Short answer

(a) The maze monsters$a$ and$c$ can be seen along the virtual hallways extending from the entrance.

(b) Each visible monster will appear 3 times in a hallway.

(c) You are at the far end of a hallway.

Step-by-step solution

Definition of reflection

The bouncing back of the ray of light after hitting a smooth platform is known as reflection. The ray that hits the surface is called an incident ray and the ray that bounces back is termed a reflected ray.

(a) Determination of the maze monsters that can be seen from virtual hallways

Show the multiple reflections of light rays from the given points in the figure.

From the above figure, it can be said that an observer can see monsters$a$ and$c$ along the virtual hallway extending from the entrance $x$. After analyzing the above figure, we can also note that the light rays from point b will reflect multiple times in the mirror maze and diminish and will not reach at $x$. This implies that, the observer can’t see monster b along the virtual hallway extending from the entrance $x$.

Thus, the light ray from point$a$ and$c$ reaches at$x$ after multiple reflections.

(b) Determination of what times the monster will appear

As each mirror is a part of equilateral triangle, three images of each visible monster will be produced.

Thus, the monster will appear three times bigger.

(c) Determination of the object that is at the far end of the hallway

Obtain the ray diagram follows,

From the above ray diagram, we can conclude that after multiple reflections from $x$, the virtual image of role="math" localid="1662993498688" $x$, that is $x\text{'}$, will get formed at the far end of hallway and then, again undergoing multiple reflections through the maze, the light rays will reach to $x$.

Thus, this implies that, you can see yourself at the far end of a hallway.