3 Perpendicular Mirrors
Suppose you walk into a room where the wall on the left, the wall in front, and the floor are all mirrors. (The walls and the floor are mutually perpendicular.)
If you hold up a ball, then how many images of the ball can you see in the mirrors?
Note
: The images shown in the figure are just the primary images.
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Each plane of reflection will not only reflect the ball, but the reflected images in the other mirrors as well.
Are we identifying partial images or only 'whole' balls?
Given that there is only one correct answer, we are being asked how many 'whole' balls (perceived whole balls) we will see in the mirrors, rather than counting individual partial secondary/tertiary images, because the number of partial secondary/tertiary images may vary, depending on our observation point.
Partial images may occur in the corners (where mirrors meet), but a single perceived ball will be comprised of the partial images in such cases - As seen below, the left and right balls are primary images, and the middle ball is actually 2 partial secondary images of the left and right primary images, but they are perceived as a single ball - The more you see of one secondary image, the less you see of the other.
While observing from within the reflection range of 2 perpendicular mirrors (I.e. not behind the mirrors), it is also possible to have an observation point where a secondary image cannot be seen in one of the mirrors (not even partially). But in this case, a whole secondary image will be seen in the other mirror. So the number of perceived whole balls created from secondary images between any 2 given perpendicular mirrors is alway equal to 1 - this is true regardless of whether it is made up of partial secondary images, or a single whole secondary image.
Why are there not an infinite number of balls?
Once an incident ray has been reflected, it wont return to the mirror again unless there is another mirror on the same axis facing the opposite direction to reflect it back.
Because each mirror is mutually perpendicular (each exclusively existing on a different axis), it will only be possible for an incident ray to be reflected off each mirror once at most.
In addition to the 3 mirrors described in this problem, the rear wall, the ceiling, and the right wall would also need to be mirrors for 'infinitely many' to be a correct answer.
Why are there 7?
If we consider that each mirror doubles the number of perceived balls (including the original ball):
We then need to account for the fact that the original ball counts as one of the 8 observed balls, but isn't counted as a reflection.
Thus, 7 whole balls are perceived in the mirrors.