Question

For the apparent magnitude ratio formula

m₁ - m₂ = -2.5 log (F₁/F₂)

I wanted to ask if the m₁ is always linked to the star with a dimmer apparent magnitude? If not, please explain

Also, with the formula stated above, is it also equal to m₂ - m₁ = -2.5 log (F₂/F₁)

Answer 1

It is not required that the m1 should be always related to a star having a dimmer apparent magnitude because it doesn't matter in the equation. This is because for a dimmer star m1 the value of F1 will be lesser than from the equation we can see that m1-m2 will be negative and the logarithm of (F1/F2) will also be negative as F1 < F2. So both the negatives will cancel out and you will get the same formula back. (It will be same as taking m2 to be the dimmer star).