Luminosity is the total power emitted by a star, whereas apparent brightness is the power received per unit area by an observer. Therefore, apparent brightness depends on both the star's luminosity and its distance from the observer.
This is part of B.1 Thermal energy transfers and is assessed at both SL and HL.
| Quantity | Luminosity | Apparent brightness |
|---|---|---|
| Symbol | ||
| Meaning | Total energy emitted per unit time | Power received per unit area |
| SI unit | watt, | watt per square metre, |
| Distance dependence | None: it is intrinsic to the star | Decreases as distance increases |
A star radiates energy approximately equally in all directions. At distance , its power is spread over a spherical surface of area . Hence,
This is an inverse-square relationship. If distance doubles, apparent brightness becomes one-quarter of its original value; if distance triples, it becomes one-ninth.
The equation also allows luminosity to be determined when apparent brightness and distance are known: . This requires isotropic emission and negligible absorption between star and observer. In most IB questions, these assumptions are implicit unless the prompt supplies information about intervening matter.
For example, consider a star with at :
Its luminosity remains wherever it is observed. Moving the observer changes only the apparent brightness. For the same star, doubling would reduce to approximately .
A common misconception is that a brighter-looking star must have greater luminosity. This is incorrect: a nearby, lower-luminosity star can appear brighter than a distant, higher-luminosity star. Apparent brightness alone therefore cannot establish luminosity unless distance is also known.
Exam technique: In a Calculate question, identify , , and , convert distance to metres, and show equation, substitution, and answer. In an Explain question, link increasing spherical area, proportional to , to decreasing apparent brightness. Do not confuse power in watts with power per unit area in .