# The Speed of Light

Whooooo! It’s the fastest you can go, the so-called “universal speed limit”.

What would happen if you went faster than that? Well, you might break reality in the process, you might travel back in time, I’m not qualified to answer that question! (who is?)

Special Relativity has a lot to say about the Speed of Light, but let’s not delve into that here (let’s try again once you’ve heard more about Inertial Frames of Reference and why Einstein had a crush on them).

Maxwell proved light is an Electromagnetic Wave, with a constant velocity of c ≈ 3*10^8 m/s (check the footer of the page if you wanna get the accepted value (I accept this one tho (it accepts me too))).

How’d he do that? Through his formulation of classical Electrodynamics with his famous Maxwell’s Equations, in which he figured out that an electromagnetic wave propagating through a pure vacuum would travel at a speed equal to $c=\frac{1}{\sqrt{{\mu}_0{\epsilon}_0}}$ where those two thingies there are the Permeability and Permitivity of free space respectively.

Wasn’t even trying to prove it, but hey, the theoretical speed happened to match pretty much  exactly with the Speed of Light. What else could light be, other than an electromagnetic wave?

What a crazy guy that guy was.

Anywhooooo, how do we know how fast light travels in the first place?

We’ve had a rough idea (a real ballpark figure) derived and measured by some guy that had a thing for the orbits of Jupiter (his name was Ole Rømer). He thought is was something like 220,000 kph – which wasn’t terrible (not great either – blew them away I bet).

My favorite way of measuring the speed of light, however, isn’t the most accurate but it is something I admire immensely. It’s called the Fizeau-Foucault Apparatus (which you can read about here) and it is shown in the diagram below.

Essentially, you have a source of light (just imagine it’s a laser pointer, whatevs (LASERS)) that shines between the teeth of a gear, being reflected right back into a camera or a detector or someshit.

Now, spin that gear, and every time a tooth blocks the light, it is no longer being reflected into the detector. As you spin the gear, the light being detected is going to flicker.

Turns out it’s not impossible to spin the gear fast enough that, when the light shines through one gap then the tooth is going to move out of the way fast enough that, by the time the light is reflected back, it shines through the next gap between teeth. Effectively, the flicker is going to diminish with the increased Rotational Velocity, and eventually it disappears completely!

Thus, you can calculate – from the speed that the gear is turning – the speed of light. Neat! (can you figure out the formula?)

There are tons of better (more modern/accurate) ways to measure the speed of light, like with the help of an oscilloscope, or with something called a Michelson Interferometer (they use these to detect Gravitational Waves!) or by using something called a resonance cavity (figuring out the resonance frequency of a standing Electromagnetic Wave, simultaneously getting the wavelength of that wave by knowing the length of the cavity, and using the Wave relation $c = {\lambda}f$ to determine the Speed of Light).

But I like the wheel way better tho; it’s retro – in a good way!