Reflection from a plane surface

For a single PLANE reflecting surface, an object placed in front of it always forms a virtual, laterally-inverted image of exactly the same size as the object, at exactly the same perpendicular distance behind the mirror as the object is in front of it. This is precisely why a reflection in a still pond, or in an ordinary plane mirror, looks left-right reversed, is the same size as you, and appears 'as far behind the surface as you are standing in front of it'.

When an object is placed between two plane mirrors inclined to each other at an angle $\theta$ (exactly the situation inside a kaleidoscope), light bounces back and forth between the two mirrors and forms several images, the exact number depending on the angle AND on where precisely the object sits. Defining $n = \dfrac{360^\circ}{\theta}$ and letting $N$ be the number of images seen, four cases arise: (I) if $n$ is an even integer, $N = n-1$, regardless of where between the mirrors the object is placed; (II) if $n$ is an odd integer AND the object sits exactly on the angle bisector, $N = n-1$; (III) if $n$ is an odd integer but the object is OFF the bisector, $N = n$; (IV) if $n$ is not an integer at all, $N$ equals $m$, the integer part of $n$. …