It turns out that people have been looking at these kinds of questions and

using geometrical optics to answer them for a very long time.

And I won't read through all of this, you might take a look at it.

But clear back in 280 BC, Euclid figured out that light had this

apparent property of going in straight lines.

Oddly, he got the direction backwards.

He thought that the light came from your eye and went to the object.

And that persisted for quite a long time.

It wasn't until about 1,000 AD that Arab philosophers got the direction right,

that light comes from an object to your eye,

which tells you the influence of expertise in maintaining, in this case, an error.

It was somewhat before that,

that they realized that light travels the shortest path between two points.

And we're going to use that fact here in just a moment.

Somewhere in the 1600s, a Dutch mathematician, who's now referred

to as Snell, figured out the law of science, and how light bent and

interfaced, and that came to be called Snell's Law, somewhat later.

And in that same time period, just a little bit later,

Fermat demonstrated mathematically this idea of the shortest

path that had been known at least 1,000 years before.

And the thing that I find fascinating is all of that was figured out before

Maxwell wrote down the fundamental equations,

which actually govern how electromagnetic waves, and therefore light, propagate.

We're going to find that rays, these things that go in straight lines,

that Euclid observed, are actually formal solutions to

the partial differential equations that Maxwell wrote down.

And yet, these people were all so smart that they were able to get to the rays and

to use them and derive properties of them,

long before they actually had the fundamental theory that went with them.