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Hello again, finally we are able to move onto the optics part of the course which is something I am very excited about
we are moving on from talking about mechanical waves and sound waves onto
electromagnetic waves and ultimately light
You'll recall when we first discussed our wave equation we also did the derivation for the EM waves
quick reminder: this is based on the 4 Maxwell's equations which governs electric field and magnetic field
combining all those, basically saying changing electric field gives rise to a magnetic field and changing B gives E
ultimately giving us
two wave equations: one for the electric field and one magnetic field
if you want a refresher
go right back and look at that video
In any case, we once again have the double temporal derivative related to the double spatial derivative
therefore wave equations we know we have travelling waves
the wave speed, of course, is given by the factor here, which is going to give us the speed of light
which is related to µ_0 ε_0 which are both universal constants in the case of vacuum
So the most common solution we will look at has the shape as illustrated here
you will see that electric field and the magnetic field
are both perpendicular to the direction of propagation as well as
perpendicular to each other
the directional propagation is given by
what's known as the Poynting vector, now this is "Poynting" with a "y", it's not a typo
due to Mr. Poynting, it's a interesting choice of last name, but it's good that he was the guy that
discovered it because the Poynting vector tells us which way the EM field
is propagating or pointing towards. How you get that is through a cross product, so you have the Poynting vector
is equal to
the E field direction cross the B field direction, so we can use our right hand rule for cross product: if we stick out our thumb
and our palm is on this side, stick out our middle finger and we have
something like that
then if the thumb points in the E
and the index finger points with the B
then the Poynting vector is in the S, you can verify that with the diagram here
so there you go, the direction of propagation given by the Poynting vector
given by this cross product here
and in terms of magnitude, we have the electric field is
c time B, because c is so big, E tends to have a much bigger number than B would, so we would often just talk about E instead
and this solution, once given the direction of the E and the direction of propagation
we've completely defined what the direction and magnitude the B would be
and on the whole is called the transverse electromagnetic wave solution
and that solution encompasses all kinds of EM waves as you can see here
all the way from gamma ray, x-ray, ultraviolet and visible, and infrared and so on and so forth
we'll be focusing mostly on the visible spectrum because it is what our eyes can look at and relate to a bit better
but the thing to notice here is because the speed of light is 3x10^8 m/s
the frequency tends to be very very high
usually for the visible light it is in 10^15, so it is not very convenient to talk about
lights in terms of frequency as we would have done for sound, instead
it's a little easier to talk about
wavelengths because it is in 100's of nm, as you can see down here, it is roughly 400 nm to 700 nm
and that's how we would often talk about visible light in terms of wavelength, of course this is wavelength in vacuum
so as you cross different medium, the wavelength is going to change, the speed is going to change as well
and therefore
we define the index of refraction
the index of refraction tells you, in any given medium
what is the wave speed in that medium and how is that correct from
your normal speed of light in vacuum which is here as c
and this n is typically greater than 1
there are some funny material that even gives you negative n, but we won't deal with that, we will stick with normal material that has
n of 1
as well
here are some sample typical ones that we often tend to use, in air, n = 1.000
something and so it's very close to vacuum
so we often take air as just having n of 1 to make things a little simpler. Water is 1.33
and then glass, depending on what type of glass, 1.4, 1.7, but 1.5 is your ball park go-to number for glass
that's the index of refraction which tells you the
ratio between the speed in different medium as opposed to vacuum
and therefore it also tells you the relation between the wavelength vs. the wavelength in vacuum as well
because the frequency stays the same
and then of course that's related to the wavelength in vacuum, and therefore, de facto for air as well