Interstellar refraction

[Tom Mazanec]

What is the index of refraction of the interstellar medium in our part of the Milky Way galaxy? How much would a light ray from M31 (which is fairly close to the plane of the Milky Way) be refracted as it enters the galaxy and reaches Earth?

[ctcoker]

The index of refraction of the ISM is so close to 1 as to not be different for all practical purposes. A photon can expect to travel a very long way before it interacts with any other particle. The dominant effects of the ISM on lght are scattering and absorption, rather than refraction. These dim and redden objects, but do not change their apparent position on the sky.

[Reality Check]

The ISM index of refaraction is tiny.
The index of refraction of a plasma is

m = (1-v_p²/v²)^1/2

where v_p is the plasma frequency (~1KHz for the ISM) and v is the light frequency, e.g. ~400–790 THz for visible light and ~GHz for radio waves.
So m is about 0.9999999999995!
There is very little refraction of a ray of light.

There is observable dispersion (spreading of the original frequency of the light) and that can be used as a probe of the ISM properties, e.g. see this chapter in The Physics and Chemistry of the Interstellar Medium about using pulsar dispersion to measure the mean electron density in the ISM.