When n(1) is greater than n(2), the angle of refraction is always larger than the angle of incidence. There are several important points that can be drawn from this equation. This is discussed in a paper published in Meteoritics and Planetary Science 34, 572-585 (1999). Where n represents the refractive indices of material 1 and material 2 and are the angles of light traveling through these materials with respect to the normal. Among the many applications of this sort of theory is the path of sound waves from meteorites hurtling through the atmosphere. The speed of sound (and hence the refractive index) varies with the temperature of the atmosphere, and hence with height in the atmosphere. And sound waves, passing through the atmosphere, are also subject to refraction via the differential form of Snell’s law. This has to be taken into account when astronomers are making precise positional measurements. For a star low down near the horizon, the refraction amounts to almost half a degree. As light from a star travels through Earth’s atmosphere, it moves not in a straight line, but in a slight curve, so that it is deviated through a few arc minutes before it reaches the astronomer’s telescope. I am thinking of Earth’s atmosphere (or indeed the atmosphere of any planet). Can you imagine a glass block of width \(a\), made of glass whose refractive index varies continuously from 1.5 at one edge to zero at the other? Not very likely, yet there is a situation that comes to mind in which there is a continuous variation of refractive index from some basal value \(n_0\) to zero. Of course these examples may seem to be very unlikely. You might like to try tracing the rays in this model. Here, too, the refractive index goes from \(n_0\) at \(y = 0\), to 1 at \(y = a\).
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