So finally, let?s talk about some modern perspectives on what light is.
It became apparent in the early 20th century
for reasons that we won?t get into the details of
that we needed to think about photons of light
which are quantized small packets of light.
These are called photons and they have been indicated again
by experiments to exist because we needed to quantize
or allow for there to be particles of light that will not just,
abstract waves of light
but instead individual packets that could be sent
or reflected off individual materials. We can ask about the frequency
and then the energy of a particular photon at a time.
So for example, if I have a photon like this one shown here
as a simple circle for representation
and it has a particular frequency to it.
We can relate that to the energy of that particular photon
via this new variable called h.
This h is a constant, so in fact it's not a variable
in the sense that it will be used in a problem as a variable.
You wouldn?t substitute h for something.
It's just a constant, just some number.
It is called Planck?s constant and the value for h is very, very, very small.
So you can see here, h is 6.6 times 10
and then a very tiny, tiny number 10 to the minus 34 joules times seconds.
So it's units of energy times time
which you can see of course just by looking at our energy equation,
E equals h times f.
So to get energy from this equation what we would do is multiply h,
which has units of energy times time,
by frequency which has units of inverse time.
So that would cancel the seconds giving you units of energy.
So of course, again, be aware that this h value is so, so small
that a particular photon has very, very, very little energy
even if it has high frequency.
These photons can correspond
to different parts of electromagnetic spectrum that we just discussed.
So for example you could have a blue photon,
something towards the higher frequencies of our spectrum
and that would have a small wavelength
but a high energy because it has a high frequency.
We could also discuss red photons which you can think of as being bigger
because they have a larger wavelength and therefore a lower energy
because they have a lower frequency.
And again, you can find the energy of either of these
by multiplying Planck?s constant h, by the frequency of the particular photon.
The photon energy equation is often expressed in a different way
so it might be useful to see what that way is.
E is sometimes written as h times omega or in fact h bar times omega.
So I want you to notice that little change that we did to our h.
What we do is simply to multiply both the numerator and denominator
of the equation for energy by 2 pi.
The reason we do this is that this factor, 2 pi times the frequency
is called the angular frequency.
So this angular frequency term is sometimes the way that we write
the energy equation for light.
So we have two new definitions here,
we have this new h which we call h bar which is simply defined as h,
Planck?s constant divided by 2 pi.
So this is just an h with a little bar through the vertical line.
And then we have this angular frequency
which is a way of not measuring per seconds or cycles per second,
but instead measuring radians per second.
So if you think about any phenomenon that?s repeating and recurring.
We can think of it as sort of a circular phenomenon
because as it goes through a full angle of 360 degrees
it comes back to where it started.
So this represent for us a useful mathematical way
of describing any repeating phenomenon
which means that it's useful also for light
since it's a way that?s also repetitive,
repetitious in nature. So this omega is again an angular frequency
which means that you have to be careful with the units.
The units are not per seconds, but in fact radians per second.
So again it's a way of thinking about this repetitive motion as an angle.
And this is a very brief discussion
by the way of the idea of angular frequency
and the way of thinking about things in an angular context.
So I?d represent if you are interested in getting into this and understanding
why this new equation for energy is written in a way it is.
To do some research in the idea of omega as an angular unit
as opposed to frequency as simply a unit of number of cycles per second.
Finally, there?s one last thing that we should be aware of
with the energy equation
which is that if I gave you the frequency of a particular photon.
You'd be able to find its energy
just by multiplying Planck?s constant times that frequency.
But if I gave you the wavelength instead,
you should be aware that you can also find the energy
just by substituting the energy, sorry, the wavelength with the frequency
using our velocity equation.
So remember we have the velocity equation for any wave.
This will include electromagnetic waves or light
and so we can rearrange that velocity equation
to say that the frequency of light is equal to the speed of light C
divided by the wavelength of the light.
And so we can use the substitution, this expression for the frequency,
to substitute in the wavelength of the light into our energy equation.
And notice very importantly that the energy equation
depends inversely on the wavelength or it depends directly on the frequency.
So this is something very important to know as a concept,
that the higher the frequency the higher the energy
but the higher the wavelength the bigger the particle
as shown in red here the bigger sort of in size of your photon if you will.
The lower the energy and so those acting the opposite sense of each other.
And this wraps up our discussion of light.
We talked only about some basic properties
as well as the polarization and then the modern view of light.
So it's not a particularly long discussion
but the concepts that we introduced related to light
as well as how to calculate some basic quantities pertaining to light
including and especially the energy for particular photons
is all that we really need to know for now
before we move to our next section.
Thanks for listening.