Re: must the number of virtual images formed by the plane mirrow be an odd one?

You are asking about virtual images formed by plane mirrors. Let me make sure I understand what that means. Suppose that I go into a room with a single plane mirror and blue ball. Light from the ball can bounce off the mirror and go into my eyes.

If I pretend that the mirror isn't there, I might interpret what I see to be a blue ball located somewhere behind the mirror.

We call this a "virtual image", because it appears behind the mirror. If I reach out my hand and try to grab the image of the ball, my hand will run into the mirror. Ouch! That can't be a real ball....

There's a rule for figuring out where this virtual image appears. A light ray leaving the blue ball must hit the plane mirror at some angle from head-on, then leave the mirror at exactly the same angle, on the other side of head-on. You may see this written as "the angle of reflection equals the angle of incidence." So, to figure out where the virtual image of this blue ball appears, just draw light rays leaving the blue ball and headed towards the mirror; the ray which bounces off the mirror and into my eyes provides the apparent position of the virtual image.

Okay so far?

Now, suppose that instead of a single plane mirror, there are two mirrors joined at some angle. Let's use an angle of 90 degrees.

Will there be any virtual images now? Well, that depends. If any light ray leaves the real ball, strikes a mirror and bounces off in just the right direction to strike my eye, then I will see a virtual image. In this example, I can draw one light ray that does exactly that: it leaves the ball, strikes the mirror at some angle from head-on, leaves at the same angle (on the other side of head-on), and goes into my eye:

So there is at least one virtual image in this situation. Can you find any light rays which leave the ball, strike the OTHER mirror, and then reach my eye? I think you can -- go ahead and try.

So there must be at least two virtual images in this situation. Are there any more ways that light can bounce around so that it leaves the real ball and ends up in my eye?

Now you know the rules. You can figure out for yourself in any situation how to find the number and location of virtual images. You can verify your friend's claim for yourself!