Let be the true zenith distance,
be the observed zenith distance,
be the observed zenith distance at layer n in the atmosphere,
be the index of refraction at the surface, and
be the index of refraction at layer n.
At the top of the atmosphere:
We define astronomical refraction, , to be:
In cases where is small (pretty much always):
A typical value of the index of refraction is , which gives R = 60 arcsec (red light).
The direction of refraction is that a
star apparently moves towards the zenith.
Consequently in most cases, star moves in both RA and DEC:
Note that the expression for
is only accurate for small zenith distances ().
At larger , can't use plane parallel approximation.
Observers have empirically found:
Of course, the index of refraction varies with wavelength, so consequently does the astronomical refraction r;
R | |
3000 | 63.4 |
4000 | 61.4 |
5000 | 60.6 |
6000 | 60.2 |
7000 | 59.9 |
10000 | 59.6 |
40000 | 59.3 |
This gives rise to the phenomenon of atmospheric dispersion, or differential refraction. Because of the variation of index of refraction with wavelenth, every object actually appears as a little spectrum with the blue end towards the zenith. The spread in object position is proportional to .
Note the importance of this effect for spectroscopy, and the consequent importance of the relation between a slit orientation and the parallactic angle.