Apparent Brightness

This formula gives the brightness per unit area that an observer measures from a source emitting luminosity L when that energy spreads out uniformly through space. As the light travels outward, it is distributed over the surface of a sphere with area 4c0d^2, so the same total power is diluted over a larger area as distance increases. That geometric spreading is why apparent brightness falls off with the inverse square of distance.

Use this when converting an object's intrinsic power output into the flux received at Earth or by a detector, such as for stars, supernovae, or other radiating sources. It is especially useful in distance estimation, comparing sources at different distances, and connecting luminosity to observational data.

• Using d instead of d^2, which misses the inverse-square dependence
• Forgetting the 4c0 factor from the surface area of a sphere
• Mixing units, such as using distance in parsecs without converting consistently when L is in watts