# Poisson stats: signal to noise

A star was measured to have an apparent magnitude m=16 with S/N=10 integrated over a minute. What is the uncertainty in the measurement?
signal=flux*area*time
noise=sqrt(signal)=sqrt(fAt)
So, S/N=sqrt(fAt)
How can I find fA?
m=-2.5logfAt+K
16=-2.5log(fAt)+K
Hoping that K is arbitrary (please verify this), I choose K=0
Then 16=-2.5log(fAt)
So fA=3.98 e-7 J/s (units inconsequential)
So, uncertainty =6.3 e-4
??
HELP!
edit:
Or, I can get N=uncertainty=sqrt(S/10)=sqrtS <--- something VERY wrong here

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I think this is an exercise in error propagation.
m=-2.5logfAt+K

You could also write m=-2.5log(I)+K
You have m, and I/dI=10. You want to find dm. (d means differential).

m + dm = -2.5log(I + dI) + K.
You could now substitute dI = I/10, and solve for m. That will work, since I will cancel.

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.

Originally posted by arcnets

However, I suspect they talk about RMS noise.
Which makes things a bit more complicated.
No, actually. You're answer if perfect. We went over this today in class. It didn't make sense then, but I think it's finally making sense. I was trying to hard to find S.