A reading series for physics-loving high-schoolers and undergraduates

Refraction That Clicks

A rod dipped in water looks broken; inside glass, light "slows" to c/1.5. Yet relativity says the speed of light is invariant. Why is that not a contradiction? Chasing the answer reveals that refraction, reflection and absorption are different faces of one complex function — and that "slow light" can be written as an effective metric of spacetime. A series that reknits the light cone of "Relativity That Clicks" and the evanescent wave of "Tunneling That Clicks" with a single thread: the refractive index.

7 episodes, complete Each: plain language → one ratio → the reveal → exercises Interactive figures / print- and PDF-ready
The spine is one sentence — what slows down is not the light but the wave made of light mixed with matter.
A photon in vacuum is always at c. It becomes c/1.5 inside glass because what travels there is a polariton, a different wave in which light and atomic polarization are mixed (Episode 1). "Slow light" can then be written as a second light cone built by the material, with refraction as a geodesic on it — the correct form of the \(c\cdot t\) intuition (Episode 2). When the index drops below 1 the phase velocity exceeds c, and information still does not: the front is always exactly c (Episode 3). Reflection comes from mismatch, and the evanescent wave of total internal reflection is tunnelling (Episode 4). Then the deepest layer — refraction and absorption are the real and imaginary parts of one complex function, glued together by causality (Episode 5). Light can be stopped, but what stops is not light (Episode 6). And to finish — everything you are looking at is a map of refractive index (Episode 7).
Download the whole series The button packs every published episode into a single ZIP.
Main sequence
Episode 1interactive figure
Light Does Not Slow Down — The Wave Does

Light travels at c/1.5 inside glass and the invariance of c is not broken, because what slows is not the photon. Waves re-scattered forward by atoms interfere with the original and shift only the phase; stack that up and you have the refractive index. The familiar "absorb and re-emit" story is wrong. n = c / vphase

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Episode 2interactive figurethe c·t view
There Are Two Light Cones

Inside a medium the light cone narrows to \(x=ct/n\). That is an effective metric: Fermat's principle becomes the geodesic equation and Snell's law falls out of geometry — exactly the "force or curvature" duality of gravity. But the causal cone has not moved, and that is what invariance of c means. ds² = −c²dt²/n² + dx²

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Episode 3interactive figure
When the Refractive Index Is Less Than One

Glass has n < 1 for X-rays, and so does a plasma. The phase velocity then exceeds c — and relativity is untouched, because information rides on the front, always exactly c. And the plasma dispersion \(\omega^2=\omega_p^2+c^2k^2\) is the dispersion relation of a massive particle. the photon has mass

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Episode 4interactive figure
Reflection Comes from Mismatch — and Total Reflection Becomes Tunnelling

Reflectance is fixed by impedance mismatch alone, and vanishes at Brewster's angle. Then total internal reflection — light does not enter, yet an evanescent wave \(e^{-\kappa z}\) seeps past. Put a second slab next to it and light gets through. That is Episode 1 of the sister series "Tunneling That Clicks." T ∝ e^(−2κd)

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Episode 5interactive figurethe core
Refraction and Absorption Are One Function

Make the index complex, \(n=n'+i\kappa\), and the real part is phase delay while the imaginary part is absorption. The two are not independent — from causality alone, knowing either fixes the other (Kramers–Kronig). So a material that refracts everywhere while absorbing nowhere cannot exist. causality → analyticity → K-K

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Episode 6interactive figure
Stopping Light — Except That What Stops Is Not Light

In 1999 light was slowed to 17 metres per second in cold atoms, and later stopped. The group velocity is set by the slope of the index, so it collapses by orders of magnitude near a sharp resonance. But what is stopped is atomic coherence — Episode 1's mixed wave, pushed almost entirely onto the matter side. v_group = c / (n + ω dn/dω)

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Episode 7interactive figurefinale
What You See Is a Map of Refractive Index

Why metals shine, glass is clear and water is blue — all of it is \(n(\omega)\). Metals are mirrors because n turns imaginary below the plasma frequency (Episode 3's \(\omega_p\)). Mirages, lenses and rainbows are all ways of reading a map of index. And to close: how the effective metric becomes a laboratory "simulation" of real gravity. the world is made of n(ω, x)

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