# Difference in Magnitudes

#### stardrop

1. The problem statement, all variables and given/known data
One star is intrinsically 100 times brighter than the other. If the brighter star is twice as far away as the dimmer star, what is the difference in their m values and their M values.

2. Relevant equations
None were given.

3. The attempt at a solution
The equation I've been using most frequently in this problem set is M + m = 5 - 5logd, but I'm not really sure how or even if I can apply it here, since this problem is reverse of what I've been given so far. Usually I have magnitudes and am asked to find the distance.

#### Kurdt

Staff Emeritus
Gold Member
The difference in magnitude between two stars given their brightness is thus:

$$m_2-m_1=2.5 \log(\frac{b_1}{b_2})$$

This relates to apparent brightness and apparent magnitude.

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