Refractive properties of media

What are the rules governing refraction? The first thing to observe is that just as with reflection, the new, bent part of the ray lies in the same plane as the normal (perpendicular) and the incident ray, (c).

(c) The incident, reflected, and refracted rays all lie in a plane that includes the normal (dashed line).

If you try shooting a beam of light at the boundary between two substances, say water and air, you'll find that regardless of the angle at which you send in the beam, the part of the beam in the water is always closer to the normal line, (d).

(d) The angles q1 and q2 are related to each other, and also depend on the properties of the two media. Because refraction is time-reversal symmetric, there is no need to label the rays with arrowheads.

It doesn't matter if the ray is entering the water or leaving, so refraction is symmetric with respect to time-reversal, (e).

(e) Refraction has time-reversal symmetry. Regardless of whether the light is going in or out of the water, the relationship between the two angles is the same, and the ray is closer to the normal while in the water.

If, instead of water and air, you try another combination of substances, say plastic and gasoline, again you'll find that the ray's angle with respect to the normal is consistently smaller in one and larger in the other. Also, we find that if substance A has rays closer to normal than in B, and B has rays closer to normal than in C, then A has rays closer to normal than C. This means that we can rank-order all materials according to their refractive properties. Isaac Newton did so, including in his list many amusing substances, such as "Danzig vitriol" and "a pseudo-topazius, being a natural, pellucid, brittle, hairy stone, of a yellow color." Several general rules can be inferred from such a list:

• Vacuum lies at one end of the list. In refraction across the interface between vacuum and any other medium, the other medium has rays closer to the normal.

• Among gases, the ray gets closer to the normal if you increase the density of the gas by pressurizing it more.

• The refractive properties of liquid mixtures and solutions vary in a smooth and systematic manner as the proportions of the mixture are changed.

• Denser substances usually, but not always, have rays closer to the normal.

The second and third rules provide us with a method for measuring the density of an unknown sample of gas, or the concentration of a solution. The latter technique is very commonly used, and the CRC Handbook of Physics and Chemistry, for instance, contains extensive tables of the refractive properties of sugar solutions, cat urine, and so on.