How do you adjust stellar magnitudes to account for elevation?

Question

I know the atmospheric extinction from 1 airmass of clean air is 0.33 magnitude. I already know how to convert elevation to airmasses.

How do I get the magnitude correction to add from the number of airmasses?

Answer 1

You have to remember that both extinction and magnitudes work in logarithmic scale; therefore loss of magnitudes is simply proportional with the number of air masses:
I = I_0 * 10^(-n k), wiht k the extinction due to one air mass;
delta_m = 2.5 lg(I/I_0)

For n=1, you get the magnitude loss for one air mass; you can figure the rest.

Answer 2

Elevation is adjusted out.