-V Govind

We all have observed what happens when light travels from air to water: it slows down, as governed by the refractive index of water with respect to air. We have conventionally chosen the value of the refractive index of vacuum to be 1, indicating that light travels at its maximum speed in vacuum, denoted by \(c\). We define the refractive index of other media with respect to vacuum, and this factor is the ratio between speed of light in vacuum and in the medium.

A fundamental question to this model would involve Einstein’s Special Relativity. The velocity \(v\) of an object of mass \(m\), energy \(E\) is given by: \(v = c\sqrt{1-\frac{mc^2}{E}}\). Einstein proposed light to be made up of massless particles of finite energy, called photons (they are not exactly particles, by the way!). If that is the case, then from the above equation, photons, which make up light, must always travel at the speed \(c\), no matter the medium we are considering. But, we observe that light slows down as it passes from air to water. How do we resolve this apparent contradiction?

First, we look at two incorrect explanations to this: (i) scattering, and (ii) absorption of light by atoms. It is stated commonly that there is a delay in propagation, due to the delay associated with scattering of light by atoms. However, one can easily see that this explanation is not quite correct, as scattering is a very random process: if light were simply scattered from atoms, it could emerge with a whole range of frequencies and velocities, which contradicts our observation of a sharp emergent beam with a well defined path, and with a well defined speed. The model of delay due to absorption also suffers from the same problem. Both these models are stochastic, while refraction seems to be a process with some ‘order’ to it.

If we imagine light as a wave instead of particles, then electromagnetic theory can offer a satisfactory explanation to this phenomenon. We know that materials are made of atoms, which in turn are made of protons and electrons as the charged particles. The assembly of many such charged particles can be thought of as a collection of dipoles. Now, for most materials, the dipoles have a natural frequency of oscillation, which is higher than frequency of visible light, so this model of slowing down of visible light will work. We treat light as an electromagnetic wave, and the oscillating electric fields of light will set charged particles in the medium to motion. The oscillating motion of these charged particles will give rise to other electromagnetic waves, which have the same frequency but are slightly out of phase with the original wave (so as to satisfy conservation of energy), as well as a different amplitude. Thus, we have the electric fields from the original light wave, as well as those from the charges in the material. We may add them to get the resultant wave. The effect is a negative phase shift in the resultant wave, compared to the original wave, appearing as the wave peaks getting ‘pulled behind,’ even when each wave travels at speed \(c\). Thus, the slowing down of light is an apparent effect due to superposition of many waves, the original light wave and the ones produced from the driven oscillators, and the math works out to give the slowing-down factor as precisely the refractive index!

However, if one demands an explanation without the use of wave theory, we will have to use quantum mechanics. Here, we consider the photon as a probability wave that can take all possible paths through the material, and can interfere with all the other photons produced within the material. The photon’s wavefunction is in a superposition, and the end result of considering all these interactions is that we get a probability wave which is ‘pulled behind,’ while the speed of individual photons stay equal to \(c\), exactly the same as the electromagnetic wave model. Due to the complicated math and less-intuitive approach of the quantum mechanical model, most people prefer the wave model in answering this question.

Referances:

• https://moviesandscience.com/blog/science/refractive-index
• https://www.youtube.com/watch?v=HZD4MR0KgQA
• https://www.youtube.com/watch?v=JZOn1B8K8mA
• https://physics.stackexchange.com/questions/466/what-is-the-mechanism-behind-the-slowdown-of-light-photons-in-a-transparent-medi