Astrophysics - Apparent Magnitude of stars in a close binary system

[goldilocks]

Homework Statement

2 solar type stars are in a close binary system. Each indivual star has an apparent brightness of m = 10 mag.

Determine the apparent magnitudes of the combined system of the 2 stars assuming they cannot be resolved as individual objects. Determine the minimum brightness for this eclipsing binary when 100%, 75%, 50% and 25% of the stellar survace are covered during the eclipse.

Homework Equations

m₁ - m₂ = -2.5 log(f₁/f₂)

The Attempt at a Solution

m1 - m2 = -2.5 log (f1/f2)
10-10 = -2.5log(f1/f2)
f1/f2 =1
f1=f2

m1+2 - m2 = -2.5 log (f1+f2 \ f2) f1 = f2
m1+2 - m2 = -2.5 log (2f1 \ f1)
m1+2 - m2 = -2.5 log 2
m1+2 = -2.5log2 + 5 mag
m1+2=4.247425011
m1+2 = 4.25 mag

Then I'm not sure how to continue from here - any help would be most appreciated!

 

[mgb_phys]

One magnitude represents a change in brightness of a factor of around 2.5
so if you double the brightness (ie two stars) the apparent mag of the combination is only going to change by less than 1mag