Index of refraction
In this Wired article, there’s a useful recap of how and why the speed of light changes in various mediums.
• Wired > “What an iPhone Lidar Can Show About the Speed of Light” by Rhett Allain (Aug 12, 2022) – Why does light travel slower in a material than it does in a vacuum?
Classically, the speed (velocity) of light depends on the index of refraction of the medium.
If you look at a material like glass, it has an index of refraction with a value of 1.52. … That means that when light is in glass, it travels with a speed that’s only 0.66 [1/1.52] times as fast as in a vacuum, with a value of 1.97 x 108 m/s.
… air in our atmosphere … 1.000273 [STP], … Water … 1.33. Diamond … 2.417 …
Using this information, Allain (associate professor of physics at Southeastern Louisiana University) demonstrates how his iPhone’s Lidar shows an apparent indentation in the wall behind a glass container partially filled with water.
So, why is the speed of light slower in various mediums?
.1. … when light enters something like glass, it is absorbed by the atoms in the glass and then re-emitted some very short time later, and this delay causes the light to travel slower. But it’s easy to see that this is wrong. Although atoms can indeed absorb light and then re-emit it, this process doesn’t preserve the original direction of the light. If this was true, the light should scatter – and that doesn’t happen.
.2. … light goes through the glass, hitting atoms and bouncing off, before eventually making its way through the material. This bouncing would cause the light to take a longer path than it would in a vacuum, where it has no atoms to bounce off. …
In this case, a light beam entering glass would also spread out as it travels through the material, due to more “collisions.” … But in order to form an image, light beams have to move through the material in predictable ways and not randomly scatter. If the light had actually scattered, you would only see a diffuse glow, instead of being able to see an image.
THE CORRECT EXPLANATION (cf. Wiki‘s)
The first thing to understand is that light is an electromagnetic wave. … An electromagnetic wave has both an oscillating electric field and an oscillating magnetic field, … as described by Maxwell’s equations. This interaction between the fields is what allows light to travel through empty space.
When the oscillating electric field from a light wave interacts with atoms in a material like glass, it causes a disturbance in the atoms. This disturbance at the electron level means that those atoms also produce an electromagnetic wave. However, the electromagnetic wave from the atoms will be out of phase with the light that entered the glass. When two waves are out of phase, their peaks are at slightly different times. The combination of the original electromagnetic wave along with the wave from the excited atoms produces a new wave – one with a slower speed.
Beating the speed of light
This “Big Think” article is a useful recap about light and the cosmic speed limit. The medium matters.
In particular, I was interested in how science communicator Ethan Siegel navigates the “is it a wave or particle” legacy language. He says: “Light, you have to remember, is an electromagnetic wave. Sure, it also behaves as a particle …”
• Big Think > “The only way to beat the speed of light” by Ethan Siegel (July 20, 2022) – No, not with popsci tachyons or wormholes.
Prisms (dense medium) and rainbows
… when light travels through a medium — that is, any region where electric charges (and possibly electric currents) are present — those electric and magnetic fields encounter some level of resistance to their free propagation [e.g., in water it’s speed is only 0.75 of that in the “empty” vacuum of space].
If the frequency stays the same [from one medium to another], however, that means the wavelength must change, and since frequency multiplied by wavelength equals speed, that means the speed of light must change as the medium you’re propagating through changes [as evident by beam bending].
The frequency of all light remains unchanged, but the wavelength of higher-energy light [e.g., blue vs. red] shortens by a greater amount than lower-energy light.
Accelerated particles and Cherenkov radiation (a “shock wave” of visible light)
… the most interesting fact is this: particles that move slower than light in a vacuum, but faster than light in the medium that they enter, are actually breaking the speed of light [over short distances sans collisons].
[As an example] The Cherenkov radiation that results, produced so long as the particle “kicked” by the neutrino exceeds the speed of light in that liquid … 
Image (in article) caption: Here, a calcite crystal is struck with a laser operating at 445 nanometers, fluorescing and displaying properties of birefringence. Unlike the standard picture of light breaking into individual components due to different wavelengths composing the light, a laser’s light is all [practically?] at the same frequency, but the different polarizations split nonetheless.
 More specifically, as Wiki describes.
Cherenkov radiation is electromagnetic radiation emitted when a charged particle (such as an electron) passes through a dielectric medium at a speed greater than the phase velocity (speed of propagation of a wavefront in a medium) of light in that medium.
Phase (info carrier wave) vs. group (envelope wave) velocity – add (superpose) waves to get a wave packet.
• George Mason University > Physics > “Phase and Group Velocity“
Dispersion is when the distinct phase velocities of the components of the envelope cause the wave packet to “spread out” over time. The components of the wave packet (or envelope) move apart to the degree where they no longer combine to complete the envelope.
2 thoughts on “When light speed changes?”
Laser pulse tricks in plasma – getting the peak of the pulse to travel faster than c. A collective “dance” vs. solo interaction.
When (laser) “pulses of photons within narrow frequencies” pass through optical media (rather than individual photons), the interference between those photons creates a wave (beat) with a group (‘wave of waves’) velocity that varies from the phase velocity.
• Science Alert > “Physicists Broke the Speed of Light with Pulses Inside Hot Plasma” by Mike McRae (02 September 2022) – Using optical wave mixing (ion-acoustic response), US physicists have demonstrated variable group wave velocity – higher or lower than c – of laser pulses in streams of plasma.
• Rochester Institute of Technology > classes > physics > “Phase and group velocities” by Michael Richmond (teaches both physics and astronomy courses and runs the RIT Observatory; acts as liaison between RIT and the WIYN 0.9m telescope at Kitt Peak).
This rit.edu lecture used images from this YouTube video:
• YouTube > meyavuz > “Group Velocity / Phase Velocity Animation – Case 1: Group Velocity larger than Phase Velocity” (Jan 20, 2013)
Here’s an article about 2d “low dimensionality” Cherenkov radiation – an effect of the “interaction between free electrons and light waves traveling along a surface” aka an “optical shock wave.”
A new experiment that “explores the quantum-photonic nature of electron radiation.” In which, for the first time, “the quantum description of light is essential to explain the experiment results.”
I’ve added [ ]’d text for clarification and brevity. The term “particle” is, as always, shorthand for localized excitation in a quantum field.
Unlike other experiments, “interaction efficiency (also called the coupling strength)” was such that “every electron emitted radiation.”
• Phys.org > “First observation of the Cherenkov radiation phenomenon in 2D space” by Technion – Israel Institute of Technology (January 18, 2023)
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