When I was attempting the derivation of the equation I started with the object on one of the mirrors. I did this because it made the working simple, and in most cases we get the correct result.
The problem with this approach is that if Ø=90° then the first image is also on the mirror, and that means the second reflection doesn't create a new image. That's why in this case we only get the object and one image. If you move the object off the mirror then it does work i.e. you get three images in addition to the object.
I guess there must be other angles where this happens i.e. an image ends up exactly on the mirror so the next reflection leaves it in the same place. It would be interesting to have a play and see if I can find any other examples of this.
Problem Solving Strategies
Problem Solving Strategies