Flux and magnitude of two stars

Statement

A star has apparent magnitude $m_1 = 2$. What flux does it have compared with a star of magnitude $m_2 = 7$?

Solution

From the definition $m_1 - m_2 = -2{,}5\log_{10}(F_1/F_2)$: $2 - 7 = -2{,}5\log_{10}\!\left(\frac{F_1}{F_2}\right) \implies -5 = -2{,}5\log_{10}\!\left(\frac{F_1}{F_2}\right) \implies \log_{10}\!\left(\frac{F_1}{F_2}\right) = 2.$ Hence $\dfrac{F_1}{F_2} = 10^2 = 100$: the first star has a flux $\boxed{100}$ times greater than the second (consistent with the fact that a smaller magnitude indicates a brighter star).

Links

Topics: Logarithmic function
Concepts: Logarithm · Apparent magnitude · Logarithmic scale
Functions: Logarithmic function
Skills: Calculate · Model
Exercise type: Modelling problem