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Today, I'm going to talk about light.
Light is an electromagnetic phenomenon, and already in the sixteenth century, way before Maxwell, a lot of studies were done of the interaction of light with water and with glass.
And the kind of experiments that were done follows -- say this is air -- I call that medium 1 -- and this is water -- call that medium 2 -- and I have a light beam that strikes this surface.
Light comes in like so -- and I define this angle as the angle of incidence, and I call that theta 1 This is the normal to the surface, and we call that the angle of incidence.
I will see now that some of that light is reflected -- reflected with an L, as in lion -- and some of that light goes into the water, and we call that refracted -- refracted, with an R, as in Richard -- and this angle, we'll call theta 2.
And it was a Dutchman, Willebrord Snellius, who, in the seventeenth century, found three rules that govern the relation between these three light beams.
The first one is that this beam, this beam, and this beam are in one plane.
As you see, that is my plane of the blackboard.
The second thing that he found, that this angle, theta three, which is called the angle of reflection, is the same as the angle of incidence.
That was known before him, of course.
And then the third one, which is the most surprising one, which is called after him, which is called Snell's Law -- although his name was Snellius -- is that the sine of theta 1 divided by the sine of theta 2, if we go from air to water, then that ratio is about 1.3.
If you go from air to glass, it's a little higher, it's like 1.5 or so.
He introduced the idea of index of refraction, which I will call N, as in Nancy -- index of refraction.
For vacuum, the index of refraction, per definition, is 1, but it's very closely the same in air, we always treat it as 1 in air.
And in water, the index of refraction is approximately 1.3, and in glass, depending upon what kind of glass you have, it's about 1.5.
And so we can now amend this law, Snell's Law, by writing here N 2 divided by N 1, N 1 being the index of refraction of the medium where you are, your incident beam -- that's why I put a 1 here -- N 2 being the index of refraction of the medium where you're traveling to.
You're refracted into this medium.
And so you see, indeed, that since water is 1.3, and air is 1, that this ratio for air to water is 1.3.
And this is called Snell's Law.
And it is immediately obvious that if you go from air to water, or you go from air to glass, that angle theta 2 is always smaller than the angle theta 1, because this number is larger than 1.
But if you go from water to air, then the situation is reversed, and that's what I want to address now, that's actually quite interesting.
So now, my medium 1 is now water, and my medium 2 is now air.
And so now, I go from here to here, and so here I have my angle of incidence theta 1 and here I have my angle of reflection, that is the theta 3, and now here, I have my angle theta 2.
And so if I write down, now, Snell's Law, then I get the sine of theta 1 divided by the sine of theta 2 is now N 2 / N 1, but N 2 is 1, divided by 1.3, if we go from air -- from water to air.
And what is so special here is that theta 2 can obviously never be larger than 90 degrees.
And so if you substitute in here, theta 2 is 90 degrees, then you will find that theta 1, then, is about 50 degrees.
And if you apply this equation, and you substitute for theta 1 an angle larger than 50 degrees, you're going to find the sine of theta 2 being larger than 1, which is nonsense.
It cannot happen.
And so nature ignores Snell's Law, and nature says, "Sorry, I can't do it," and what nature now does, if the angle of theta 1 is too large -- in this case, with water, larger than 50 degrees -- this is not there anymore, and all the light is now being reflected off that surface.
And we call that total reflection.
Total reflection.
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