# Flux, luminosity and stellar magnitudes

> Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).

Course: [Stars, distances and stellar evolution](https://studybrix.com/en/courses/stellar-astronomy/index.md)
Level: university
Prerequisites: Logarithms and inverse-square relationships.

## Notes

### Luminosity and flux

Luminosity is emitted power; flux is received power per area. For isotropic emission with negligible absorption, F=L/(4πd²).

### Magnitude

Magnitude differences use a logarithmic scale: m2−m1=−2.5 log10(F2/F1). A smaller magnitude denotes a brighter source in the same band.

### Absolute magnitude

Absolute magnitude compares sources at the conventional distance of 10 pc. Bandpass and extinction assumptions must be specified.

### Distance modulus

Ignoring extinction, m−M=5 log10(d/10 pc). Dust can dim and redden a source, so uncorrected brightness is not purely a distance indicator.

## Practice questions

### 1. For equal luminosity and negligible absorption, one source is twice as far away. Find its flux divided by the nearer source's flux.

Answer: 0.25

Explanation: The inverse-square law gives 1/2².

### 2. A source becomes 100 times brighter in the same band. Find mnew−mold.

Answer: -5

Explanation: −2.5 log10(100)=−5.

### 3. Which quantity describes emitted power rather than received power per area?

A. Luminosity
B. Parallax angle
C. Apparent magnitude by itself
D. Flux

Answer: Luminosity

Explanation: Luminosity is intrinsic emitted power under the model.

### 4. Ignoring extinction, find m−M for d=100 pc.

Answer: 5

Explanation: 5 log10(100/10)=5.

### 5. At which conventional distance is absolute magnitude defined?

A. 1 km
B. 1 AU
C. 1000 light-years
D. 10 pc

Answer: 10 pc

Explanation: Absolute magnitude standardizes the distance at 10 parsecs.

### 6. Why can two equally bright-looking stars have different luminosities?

Sample answer / marking guidance: Their distances and intervening extinction can differ. The received flux alone does not uniquely determine luminosity.

Explanation: Credit distance and at least the possibility of absorption.

### 7. If two sources have the same flux but one has distance 3 times the other, find the luminosity ratio for the farther source.

Answer: 9

Explanation: At equal flux, L scales as d².

### 8. Why must a magnitude comparison specify the bandpass?

Sample answer / marking guidance: Different spectral energy distributions yield different relative brightness in different bands. A magnitude without a consistent band can mislead.

Explanation: Credit wavelength-dependent measurement.

## Further reading

- https://science.nasa.gov/universe/stars/

Original AI-assisted educational draft; not independently teacher-reviewed. References support further study, not copied exercises, affiliation or curriculum accreditation.