# Computing differential refraction

Version: 1.0 2003-03-12 Ivo Saviane

The differential refraction between two different wavelengths and is computed (in arcseconds) as

where is the refraction index of air at wavelength , and is the zenith distance. Since is always close to , is used instead, in order to make computations easier. The computation of the refraction index is streamlined by first computing the index for dry air in standard conditions, then correcting for a different pressure and temperature, and finally adding the contribution of humidity.

## 1.1 Standard conditions

Standard pressure, temperature and humidity conditions are defined as , (i.e. ), and dry air. At high altitudes the pressure is smaller, and one can guess the value of pressure as , where is the scale height of the atmosphere (typically ). However, for La Silla we have actual measurements, just have a look at the meteomonitor''. Thus a typical value can be .

## 1.2 Refraction index in standard conditions

We call the refraction index of air, in standard conditions, and compute it as:

where the wavelength is expressed in nm.

## 1.3 Refraction index in other conditions

Then for other temperatures and pressures, the refractive index in dry air is given by

## 1.4 Refraction index in presence of water vapor

If there is water vapor in the air, and its pressure is , then the refractive index is smaller, and it is computed as

Normally one has readings of relative humidity , not of water vapor pressure, so the latter is computed as

where is used to convert from millibar to Pa, and is the saturation pressure of water vapor, which in turn is computed (in millibar) as

where is the tempeature in Celsius (so ). A typical vapor pressure is .