Field
Optics
Light, and the small number of rules it obeys.
The bend at the boundary, and what it is really about
Light changes direction when it changes speed. Snell's law is the geometry of that statement, and it can be derived without knowing anything about light at all.
What a lens is doing, and why three rays are enough
A lens bends every ray that reaches it. The construction uses three, because three are all that can be drawn without calculation — and any three that meet prove all the rest do.
The angle past which light cannot leave
Snell's law asks for the sine of an angle greater than one, and no such angle exists. What happens instead is a perfect mirror made out of nothing but a change of speed.