The way that electromagnetic radiation or light exchanges
energy with objects, is mostly through the electric field.
What happens is, the electric field of the light that's coming in acts on
the charged oscillator of the the object that we're talking about.
And if the frequency is the Greek letter Nu,
the frequency of the light is pretty much
the same as the frequency of the this oscillator.
Then the energy from this light being carried
to the vacuum can be dumped into this oscillator.
And you can heat the thing up through the vacuum.
We're going to talk about the light that comes off of an object.
Because this is a two-way street.
If the light can come in and be
absorbed by this oscillating piece of matter,
if you have this matter being oscillated just because it's warm,
it can also create light and send it back out.
And so we're going to talk about the kinds of light that this object emits
by thinking about a spectrum.
Which is a plot of how bright the light is
as a function of the different frequencies, or wavelengths, or colors,
or however you want to describe the different kinds of light.
It's a plot that looks kind of like this.
It's got an Intensity on the vertical axis.
And then we're going to use wave numbers on the horizontal axis
as our index of "colors".
The units on the Intensity axis are watts per square meter, per wave number.
And the reason why that's done is because that way if you have
a range of light color say between one and two wave number units.
One and two waves per centimeter, for example.
Then the area under this curve is going to be equal to
watts per meter squared per n times n, and the n's would cancel.
Leaving us just with a total of watts per square meter.
So that means that these plots are drawn so that the area under the total curve is
the total energy leaving the object, in nice units that you now
understand, of watts per square meter of the surface of the object.
So what those spectra look like, are these sort of humps.
I've drawn three of these different humps.
This one's sort of off of the top of the chalkboard there.
Because you get different curves depending how warm
the object is. Ss the object,
gets warmer, the peak energy, which is where the intensity is the strongest,
shifts in this direction, toward shorter wavelength, or higher wave number,
more energetic light.
So you probably have known this before by
thinking about the idea of red hot and white hot.
An object just at room temperature is shining light.
But it's all in the infrared, so we can't see it
with our eyes that can only see in the visible range.
But as the object gets hotter and hotter,
the tail starts to encroach in the visible range, and
you start to see some red color there.
And then if it gets really hot, it can
fill up the whole visible range, and that's when something gets white-hot.
White hot is much hotter than red hot.
You already sort of knew that, right? The other thing about this
spectrum is that it gets much bigger as you get hotter.
And it turns out that there's a formula describing this.
It's right here.
The total energy in watts per square meter is given by these three terms.
The first is Epsilon which i'll explain next.
the second is the Stefan–Boltzmann constant which
is just a constant number you can
look up in a book, it never changes.
And then third, is the Temperature in Kelvins raised to the fourth power.
So you raise it to the fourth power.
That means if you double the temperature, the energy flux goes up by a factor of
two to the fourth, which is 16, so
it's a very, very powerful function of temperature.
So, back to this term now, Epsilon.
This relates to
whether the object is what they call a black body or not.
if an object is a black body, it's as though
it's a musical instrument that has all of the notes.
Like a piano that has all the keys, if you
just hit it with a big hammer or something.
Make all of the keys vibrate at once.
You'll get this big wall of sound like this.
But if you have a piano that's missing a bunch of strings in the middle and you do
the same thing, you'll get some low notes and
you'll get some high notes but there will be some
missing stuff in the middle.
So this is what a physicist would call a black body.
Because it makes a smooth black body curve like this.
And the Epsilon value for this would be one.
So you'd put in number one here.
And there's no units to Epsilon it can go
to zero if an object had none of these oscillators,
and couldn't make any infrared light at all,
to one, if it had all of the notes and could make all the different frequencies.