Flux Ratio from Magnitude Difference

\[\begin{aligned} R &= 10^{0.4(m_2-m_1)} \\ F_1 &= F_2 \cdot 10^{0.4(m_2-m_1)} \end{aligned}\]

Variables

Rflux ratio between object 1 and object 2

F1flux of object 1

F2flux of object 2

m1apparent magnitude of object 1

m2apparent magnitude of object 2

Description

What is this formula?

This formula calculates the flux ratio between two astronomical objects from their apparent magnitude difference. Because the magnitude scale is logarithmic, a small magnitude difference can represent a large difference in observed flux.

When to use it

Use this formula when comparing the observed brightness of stars, galaxies, planets, or other celestial objects using apparent magnitudes.

Example

Object 1 has an apparent magnitude of 3 and object 2 has an apparent magnitude of 5.

Data:

m1 = 3

m2 = 5

Formula:

R = 10^(0.4(m2-m1))

Substitution:

R = 10^(0.4(5-3))

R = 10^0.8

R = 6.31

Result:

Object 1 has approximately 6.31 times the observed flux of object 2.

Applications

- Photometric astronomy

- Star brightness comparison

- Telescope observation analysis

- Variable star studies

- Galaxy brightness measurements