Astronomy Principles and Practice Fourth Edition.pdf

Atmospheric refraction 113
Figure 10.1. Refraction of a light beam by a slab.
Figure 10.2. Refraction by a series of slabs.
The second law (Snell’s law) states that
sin i
sin r = n (10.1)
where n is called the index of refraction of the substance making up the slab. Since r < i, n > 1.
If YCZ is the normal at C, YCB = MBC = r (PQ being parallel to RS) and hence, since
ray paths are reversible, ZCD = i. In other words, the emergent ray CD will be parallel to AB but
not collinear with it.
For a number of plane, parallel slabs of indices of refraction n 1 , n 2 , n 3 ,...,n j , we can extend
relation (10.1). In figure 10.2, the ray of light passes from slab 1, of refractive index n 1 ,intoslab2,of
refractive index n 2 . Then by Snell’s law,
sin i = n 1 sin r 1 .
Also, for the second slab,
Hence, for j slabs, we have
sin i = n 2 sin r 2 .
sin i = n 1 sin r 1 = n 2 sin r 2 = n 3 sin r 3 =···=n j sin r j . (10.2)