The internet is a very powerful tool, putting
the knowledge of humanity at our very fingertips.
However, the internet is also a source of
misinformation.
You can hear all sorts of explanations, stated
authoritatively, and with good intentions,
but also utterly and totally wrong.
So, in this video, I thought I’d address
a common one and give a correct explanation
for why light slows down in water.
Actually, that’s just a catchy title.
I want to tell you why light slows down in
any transparent medium- certainly water, but
also glass, plastic, and even air.
If you ever took a physics class, you learned
about the index of refraction of a material.
The index of refraction is just a fancy term
for how much light slows down in that material.
The index of refraction, always written as
little n, is a number greater than one.
And the speed of light in a material is just
the speed of light in a vacuum, divided by
the index of refraction.
I put a table here to give you a sense of
how much light can slow down in common materials.
This slowing down is the reason that objects
look bent when stuck in water.
It’s because the path that light follows
bends when it enters or exits water.
It’s the reason that you can get pictures
like this one here.
And I should let you know that no physics
teachers were harmed in shooting that photo.
There’s a ton of interesting phenomena I
could show you that arises because of the
index of refraction and the slowing of light,
but I want to focus entirely on the slowing
thing.
So, to do that, let’s look at this animation.
So suppose you have a piece of glass with
index of refraction equal to 1.5.
That means that light will travel at 2/3 the
speed of light in the glass.
If you shoot a laser at the glass, the light
from the laser will travel at the speed of
light until it hits the surface of the glass.
When it hits the surface of the glass, the
light will slow down to 2/3 its original speed
and it will change its direction.
Once the light gets to the other side of the
glass, it will emerge from the glass, change
its direction, and move again at the speed
of light.
That’s what happens.
In addition, the light emerging from the glass
will travel in exactly the same direction-
well, more precisely, in a path that is parallel
to the direction of the incident light.
The path is offset a smidge to the left, but
the angles are the same.
So that’s what happens.
It’s been tested and there's no debate on
any of that.
So now for the real question.
Why does the light slow down?
And how can it speed up again when it leaves?
There are two very common explanations that
you find on the internet and both of them
are completely wrong.
Let me tell you them first.
The first one makes kind of some sense.
It’s wrong, remember, but it does make sense.
It's the idea that light scatters off atoms
as it passes through the glass.
The light hits an atom and goes careening
off at an angle, then hits another atom and
careens off at a different angle.
Light always travels at the speed of light
between atoms.
That process occurs again and again as the
light passes through the glass, but let’s
focus on just these two scatters to see how
the explanation goes.
If we take away the atoms, we can see the
important bits.
There is the actual path traveled by the light
in this scenario, which we can compare to
the straight line path.
If we straighten out the actual path, we see
that it is longer than the straight line one.
And, if light travels at the speed of light
in a vacuum between scatters, we see that
it will take longer that it would take if
it went the straight line distance.
Taking longer is another way of saying effectively
going slower.
And this is how some people explain the effective
slower speed of light in glass.
So how do we know it’s wrong?
Well scattering isn’t a precise process.
Light can scatter in lots of directions.
For instance, it could have scattered like
we see here.
This is a much more serious scatter, with
a much longer path, and consequently, light
would effectively be much slower if this happened.
Furthermore, there is no way to guarantee
that the light would end up back traveling
in the original direction.
In fact, if light did what is being claimed,
it wouldn’t follow the path we observe.
Instead, light would come out of glass with
a range of velocities and a range of angles.
This idea just doesn’t work because it doesn’t
make correct predictions.
So, no good.
The second wrong idea is that light is not
scattered, but rather that it is absorbed
and re-emitted by atoms.
Between atoms, the light travels at the speed
of light in a vacuum.
The amount of time the atom takes to absorb
and emit the light seems to slow the light
down.
You can see what I mean in this example here.
The speed of the photons while moving is always
the same, but the time taken during the absorption
and emission makes the solid line take more
time than the dashed one.
This effectively makes light slower.
Now this idea, while sensible, is also wrong.
Let’s see why.
The problem is that when an atom has been
absorbed by a photon, it doesn’t remember
where the photon was coming from.
And when it emits a photon, it can do it in
any direction.
So what really would happen in the absorption/emission
case is something more like this.
The photon would be absorbed and reemitted
in a willy-nilly direction.
In the end, the passage of light through the
material would end up looking like this, which,
well, isn’t what we see.
So, if neither of these ideas work, what does?
First, I should say that these two ideas kind
of have buried deep at the bottom of them
the idea that light is a particle.
However, the reason that that light slows
down in material is better illustrated if
one embraces the idea of it being a wave.
There are many properties of a wave, most
importantly, the wavelength.
The wave oscillates up and down, with a separation
between peaks and a time between oscillations.
A second important property is what we call
superposition, which is just a fancy way to
say that you can add them.
And adding them is easy.
You just take the height of the two waves
and add them together.
If the two waves are lined up so the peaks
are at the same place, the result is a single
wave with a higher peak.
If the wave is lined up so a peak corresponds
to a trough, then the two waves cancel.
And, if one wave has a different wavelength
than the other, you end up with a funny looking
shape.
That’s just how it works.
It gets more interesting when one wave is
moving at a different speed than the other
one.
The result is a different wave, but one that
has a different speed than either of the two.
That’s super important, so let’s just
take a careful look at it.
If we add the two top waves, which have different
speeds, the bottom wave also moves, but slower.
So let’s get back to light moving through
glass or water.
Remember that light is a wave of electric
fields.
It oscillates with a characteristic wavelength
and frequency.
That wavelength depends on the color of light,
with blue light being about 400 nanometers
and red light being about 700.
The numbers don’t matter as much as that
you remember that light is changing electric
fields.
Now of course glass is made of atoms, which
are surrounded by electrons.
Electrons have an electrical charge and that
charge feels a force from the oscillating
field of light.
Because it feels a force, the electrons move.
But moving electric charges also set up their
own oscillating electric field.
Said simply, the oscillating electric field
of light makes electrons move which make a
second oscillating electric field.
And, if you have two oscillating electric
fields, that's two oscillating waves and you
can add them together just like we saw before.
The net effect is that the two waves combine
and make a single wave of oscillating electric
fields.
And that is the wave that moves through matter.
And- and this is important- it moves at a
slower speed than light does in a vacuum.
This also explains something that many people
were confused by.
Most people were willing to accept that passing
through glass would slow down light.
But they were very puzzled about light speeding
up when it left the glass.
That seemed like it created energy and, well,
that didn’t make any sense.
But now I hope it does.
Before light hits the glass, it travels at
the speed of light in the vacuum.
When it passes through the glass, the light
causes the electrons to move and generate
a second wave that adds to the light.
Light still moves at the speed of light in
a vacuum, but the wave from the electrons
move at a different speed, and the combined
wave moves slower than light would if the
atoms weren’t there.
Then, when light leaves the glass, there are
no atoms around to make electric fields to
add to light and then light speeds along at
the preferred vacuum speed.
So that’s it.
Light effectively travels slower through material
because when it is in material it generates
a second wave that combines with light and
the combined new wave moves slower than the
familiar speed of light.
Ta da!
Alright, so tell everyone.
This is something for which you often hear
wrong explanations on the internet.
But now you know and that means you’re eligible
for membership in the physics cool kids club.
Well, that was pretty awesome.
I hope you remembered to like, subscribe and
share.
I always love to find out the underlying answer
for how things work- especially when you often
find wrong explanations online.
But, as is often true, the way to find out
the right answer is to learn some physics,
because, well- as I’m sure you'll agree-
physics is everything.
