# How does every ray of light or photon can follow the same Snell's law in a very random states of matter like gases and liquids?

We know that to study refraction at the interface of two media, we use Snell's law which is $$μ=\frac{\sin(i)}{\sin(r)}$$ or $$μ=c/v$$ (for vacuum as one of the media).

I know this is an experimentally proved law, but the one thing I don't understand is that every time a light ray passes through an interface between two media it gets refracted by the same angle for the two particular media. Now if we see the second formula, we can understand that for example when a light ray passes from, say vacuum to any other medium its velocity decreases because of the fact that it takes time for light for it to be absorbed and then emitted by any particle. But it still moves with velocity $$c$$ in the empty space in the medium. The thing I don't understand is that, why such random systems like liquids and gases do not give random results for refracting angles.

## 1 Answer

Typical photon of visible light has spatial size no smaller than its wavelength, which is several hundreds of nanometers. If there is no process that would localize the photon, it can have even bigger spatial extent due to quantum delocalization. Molecules are usually considerably smaller. For example water molecule has only 0.3 nm. So the photon feels only spatially averaged electric fields of the medium. Moreover, the length of the medium the photon crosses in the direction in which its travels is even much larger than the photon wavelength, which adds to the averaging argument.

For highly energetic photons with smaller wavelengths (x-ray, gamma), we are more likely to observe scattering of the photon from individual electrons or nuclei rather than from the interface of two environments with different refractive indices.

When light ray passes from, say vaccum to any other medium its velocity decreses because of the fact that it takes time for light for it to be absorbed and then emitted by any particle.

I do not think this is accurate, the velocity in medium is not decreased because of repeated absorption/emission, but because the electric charges in the medium respond to electric field in the photon by emitting secondary wave that interferes with the electric field of the original light (Wikipedia).

• So for shorter wavelengths like x rays would not follow snell's law if that's the case – Sourabh Feb 24 '19 at 19:02
• For X-way, there will still be photons that react on the medium boundary and follow Snell's law. But many photons will also be absorbed or scattered by individual molecules. So it is closer to "reacting on random states of matter" than visible light. – Irigi Feb 24 '19 at 19:28
• "Typical photon of visible light has spatial size no smaller than its wavelength" We don't know anything about the size of a photon, only about its probability distribution. – my2cts Feb 24 '19 at 20:25
• Right, would it be better to write "photon of visible light is delocalized over area no smaller than its wavelength"? – Irigi Feb 24 '19 at 20:31