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REFERENCES
How Maxwell found speed of light:    • Why is the speed of light what it is?...  
Why Isn't Speed of Light Infinite?    • Why isn't the speed of light infinite...  

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CHAPTERS
0:00 Einstein's Special Theory of Relativity
1:23 Skillshare: How to make animation like this
2:40 Why is the speed of light constant?
4:30 Speed of light changes but not photons
6:05 Why light seems to slow down
8:39 Quantum Mechanical Description

SUMMARY
Why does the speed of light change in different media? or Does it? How photons always travel at the same speed, but the speed of light changes.

In 1905 Einstein proposed the theory of special relativity. One of the postulates was that that speed of light is the same in a vacuum, the speed of light constant. But in other media, like water or glass, the speed of light changes. This is the reason we can see a bending effect when putting a straw in a glass of water, and the pattern of colors when light goes through a prism. But while the speed of light we perceive changes, the speed of the individual photons making up the light does NOT change.

Why is the speed of light constant. One way to explain this is to look at Maxwell’s equations. It states that the speed of light is due to the properties of space time. Since these properties do not change, the speed does not change. This is the logic Einstein used to formulate his theory of special relativity.

Any light traveling at an angle changes direction due to a change in its speed. So for example, when light travels from air into water, it slows down, causing it to continue to travel at a different angle, and this leads to refraction of the light which is the distortion that you see. But although the light that you perceive slows down, the photons making up the light are not slowing down at all.

Light is an electromagnetic wave. Electromagnetic waves are composed of changing electric and magnetic fields. Changing electric fields induce magnetic fields and changing magnetic fields induce electric fields, and together they make electromagnetic waves. One quanta of such a wave is a photon.

Unlike empty space, substances such as water and glass are made up of charged particles. Why charged? Well, they are made up of atoms, and atoms contain positively charged protons and negatively charged electrons.

Charged particles are affected by changing electromagnetic fields. We also know from Maxwell, that the movement of electric charges creates an electromagnetic field of its own. Specifically the movement of electrons, creates photons. Photons are light, the movement of the electrons emits a light of its own.

These are induced electromagnetic waves, and they are at various wavelengths. Most of these induced light waves cancel each other out, except the ones traveling in the same direction as the original light wave.

Each of these induced light waves, which again are streams of photons, travel at the same speed, c. This is called their phase velocity. However, what we actually see with our eyes is not these individual waves of light, but a mixture or summed up wave of light. In other words, the induced light waves interact with the original undisturbed light wave that entered the substrate. Since the light waves are at different wavelengths, there is constructive and destructive interference in parts of this summed up mixture of light. And this summed up light wave in glass and water, it so happens travels slower, that is, LESS than c, the maximum speed of light.

So the apparent speed of light, that is, what we see with our eyes, is the group velocity, or a summed up wave slower than c, even though all individual waves are traveling at the maximum speed. This is the reason that no acceleration or speeding up of individual photons occurs after the light leaves the substrate. In fact, the photons had been traveling at the same maximum speed the whole time.

Quantum mechanical picture: In a nutshell, the summed up group velocity of light, in quantum mechanical terms, is due to the superposition of all the various paths that the undisturbed light can take and its interactions with all the atoms of the medium.
#speedoflight
The photon takes every possible path and interacts with every atom, and all the induced photons created. And what we see as a result is the superposition of these paths and interactions. These photons by following every possible path ends up interfering with itself and other photons in such a way that it creates the net effect of a wave that travels slower than the speed of light. The result is identical to the classical picture I described earlier, but the details are different.