Something Fishy

The other day, I happened to glance through the peephole of Marika's apartment into the building's lot:

It got me thinking about the wide, but distorted image you get from them, and I thought I'd talk a bit about the optics behind it.

Lenses use refraction to bend light in specific ways.  When a beam passes from one material to another, it changes direction according to the properties of the two substances.  The angle of the change is determined by Snell's law (diagram from Wikipedia):

I've mentioned refraction before, in the context of the Principle of Least Time.  The general rule for refraction is that when a beam passes from a material with lower index to higher index (like air-to-glass) the beam bends toward the perpendicular, and when it passes from higher to lower index, it bends away.

Peepholes use a type of fisheye lens to gather lots of light from the outside, and focus it into a smaller area that can enter your eye:

At the same time, if you try to look from the other side of the door,  all the light from a small spot gets spread out:

That makes the lens essentially one-way, allowing you to see outside, without others seeing inside.  It seems strange to me that we call something designed for privacy and security a "peephole" when the other uses of "peep" I can think of (outside of Easter) are so salacious: "peepshow" and "peeping Tom".  I suppose that's why I'm sticking to physics!