I've been reading up on apparent magnitude and luminosity, and have tried using some of the formulas that I've read about to calculate some of the apparent magnitudes of common stars, and it doesn't seem to be working too well.
So, according to Wikipedia,
where Fx is the observed flux in the passband x, and F0x is a reference flux.
In turn, flux can be calculated as:
where L is the luminosity and r is the distance between the source and the observer.
So, I tried calculating the flux of Vega, for reference, using the values for luminosity and distance found on Wikipedia (I converted to Watts and meters):
and then calculated the flux of a test star, in this case Fomalhaut:
But then when I put it into the formula:
But, Fomalhaut's apparent magnitude is supposed to be 1.16.
I'm obviously doing something wrong, but I can't figure out what.
Any help would be much appreciated!