Hey Crazies.
This mirror reflects all visible light,
but so does this piece of paper.
What’s the difference? Why aren’t they the same?
I actually get this question a lot in the comments.
Let’s see where it takes us.
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Alight, so the quick answer is that there's two different kinds of reflection.
The mirror sends the light in a very specific direction.
We call this specular reflection
because “specular” means “mirror” in Latin.
With this type of reflection, you see a different image depending how you look at the mirror.
The image changes as you move around a room.
It gives you the illusion you’re looking through a window into some mirror universe.
Paper is a little different.
With paper, the light scatters instead.
It spreads out, so we call it diffuse reflection.
If you move around the room, you’ll keep seeing the same thing:
White.
The word reflection is pretty fitting for both types though.
It comes from the Latin “reflectere” meaning “to bend backward,”
which is exactly what both types of reflection do.
They bend the light backward, but in very different ways.
They’re going to end being the same, aren’t they?
Yep. You’re finally learning.
Ok, so you’re probably wondering how that’s possible.
How could these two different phenomena be the same?
Well, the usual explanation goes something like this.
A mirror is incredibly smooth, even under a microscope,
so the surface always faces the same direction.
But, with something like paper, the surface has tiny imperfections.
The light still obeys the law of reflection at each separate spot,
but different spots face different directions, so the light scatters instead.
It sounds pretty convincing,
except it can’t be the whole story.
If it were, a rough piece silver would look white
and it doesn’t.
But it’s definitely part of the explanation.
I mean, all of us can tell this smooth piece of plastic is not a mirror,
but it definitely has some mirror-like effects.
It’s just not the whole explanation.
There must be something else going on here.
Hmm.
We’re going to have to go deeper,
like, literally deeper into the material.
Super zoom!
The mirrored surface is made of atoms, usually silver or some other shiny metal.
We like to imagine that light interacts with the atoms on top,
but there are spaces between those atoms that the light can fit through.
Scattering can happen off many layers of atoms and still contribute to the reflected light.
The mirror-like reflection in this plastic is from the surface atoms.
The color is from the layers underneath.
And that’s not even considering the wave nature of light.
If we do that, each of those atoms sends out its own light in all directions,
including into the material.
Ultimately, those light waves cancel except in two specific directions.
You heard me right.
The incoming beam splits in two at any surface.
It doesn’t have to be transparent.
Some of the light will reflect.
We call that the reflected light for obvious reasons.
The rest will move forward into the new material.
We call that the transmitted or refracted light.
How much is reflected or transmitted depends on lots of things:
The materials involved, the incoming angle, the frequency of the light, etc.
For an air-glass boundary, the light is about 5% reflected and 95% transmitted,
because transparency.
For a mirrored surface, it’s the other way around.
The point is there’s always some transmitted light,
even for a mirror.
What makes these materials different is how far that transmitted light can go.
It’s something we call Penetration Depth.
[Boing Noises]
This penetration depth depends on four things:
The electric and magnetic field properties of the material, the frequency of the incoming light,
and, most importantly, the electrical resistance the material can provide.
The three material properties are just numbers you look up in a table,
like this one from Engineering Toolbox.
As always, links in the doobly-doo.
I calculated a couple of these depths just so you can get some perspective.
The penetration depth for glass is 156.5 meters.
That’s over 500 feet.
For a silver mirror, it’s 1.4 nanometers.
That’s drastically different from glass.
So it goes that far and just stops?
Well, no.
The light intensity drops off exponentially.
A penetration depth of 1.4 nanometers means that,
for every 1.4 nanometers the light goes into the silver,
the intensity goes down by a factor of e.
At one penetration depth, the intensity is 37% of the original.
At five penetration depths, the intensity drops below 1%.
For the silver mirror, that’s still only 7 nanometers.
That transmitted light is going nowhere fast.
Based on this equation, we can see transmitted light won’t go as far in electrical conductors.
That’s what gives metals that distinctive metal coloring we all recognize.
The light barely penetrates.
So, why aren’t all insulators transparent?
Oh. Uh. Uh. Whoops!
There’s one more issue we have to resolve.
These atoms need energy to send out their own light.
It doesn’t come out of nowhere.
Energy must be conserved.
Conservation of energy shall not be violated!
That incoming light is absorbed and used,
but there’s a catch.
There are two different ways that light can be absorbed by those atoms:
Resonant Absorption and Dissipative Absorption.
I know. I know. Those are some serious 10-dollar words,
but they’re not as fancy as they sound.
Resonant absorption is when a single electron absorbs a single photon
with just the right energy needed to bump the electron to a higher energy level.
This is the kind of absorption that results in things like fluorescence and phosphorescence.
This is not the kind of absorption that creates reflected and transmitted light beams.
I repeat.
Resonant absorption does not create reflected and transmitted light beams.
When this happens, the electron usually doesn’t have a chance to re-emit that light.
It gets stolen by neighboring atoms as heat instead.
This is the light that heats up a material.
Fluorescence and phosphorescence are just special exceptions.
Reflected and transmitted beams come from the other type of absorption:
Dissipative Absorption.
This type doesn’t require quantum mechanics. It is a very classical effect.
An atom is just minding its own business when some light comes along.
Because the atom is made of charge, the light’s electric field drives the atom’s motion.
The atom vibrates at the same frequency as the light.
Vibration is a kind of acceleration and accelerated charges emit light.
This vibration causes the atom to send out its own light,
which combines with the light from other atoms.
How all that light combines depends on things like atomic spacing, response lags,
vibrational damping and resonances.
That’s too many things for our brains to handle,
so we take that overwhelming amount of information and summarize it as a single unitless number:
the refractive index.
That’s another number we can just look up in a table somewhere.
If we have that number, we can forget atoms and molecules even exist.
All we need to know is the type of material and we’re good to go.
Just keep in mind, this refractive index depends slightly on the frequency of the incoming light.
Different kinds of light can transmit or reflect better than others.
That’s what gives everything their color.
Even off of a mirror, green reflects better than other colors,
which is why, if you look deep into mirror infinity, things tend to start turning green.
So why isn’t everything a mirror?
Well, a few reasons.
First, the surface has to be really smooth.
Too many imperfections and the light will scatter.
Second, the surface has to be a good electrical conductor.
That way the light barely penetrates.
Silver is the best, but it’s also expensive,
so a lot of mirrors are made of aluminum instead.
Lastly, the light shining on the surface can’t match the quantum energy gaps of the electrons,
otherwise the light is destined to become heat rather than a reflection.
If you check all those boxes, you’ve got yourself a mirror.
If not, it’ll just be a solid color.
So, got any more questions about mirrors?
Please ask in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s ok to be a little crazy.
Several of you asked if anyone had ever done diffraction off of a mirror.
Oh yeah, for sure.
I actually had to do it as a lab in Modern Physics in undergrad.
It’s totally a thing.
A nice reflective metal ruler is basically a diffraction grating.
Feel free to try it at home if you've got one.
And thanks for watching!