If star A is 14.5 times brighter than star B, then what is their magnitude difference? A) 1.2 B) 2.9 C) 63.1 D) 800 E) 6.2 × 10⁵

Question

Quizplus · Accepted Answer

The magnitude difference between two stars is given by:
$2.5 \log_{10}(\frac{F_{B}}{F_{A}})$
where $F_{A}$ and $F_{B}$ are the fluxes of the two stars.

Let's assume star B has magnitude m. Then, star A has magnitude $m - 2.5 \log_{10}(14.5)$.

The magnitude difference is then:
$2.5\log_{10}(\frac{F_{B}}{F_{A}}) = 2.5\log_{10}(\frac{F_{B}}{F_{B}/14.5}) = 2.5 \log_{10}(14.5) = 2.9$.

Therefore, the answer is B.

If Star a Is 14