Luminosity Spreads by Distance Square - Observational Astrophysics: Distance, Flux, Transits, and Spectra Step by Step

The inverse-square law says flux equals luminosity divided by the area of a sphere, expressing a purely geometric fact: the same luminosity spread over a growing sphere dilutes per unit area. It assumes a point source radiating into transparent space, so absorption or extended structure will bend the relation. Flux is measured with its own error bars; luminosity and distance are inferred under the model, never read off directly.

A normalized inverse-square flux ledger keeps luminosity and distance tied. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Distance is squared before flux is computed

The source luminosity is 16 watts and the distance is 2 meters, so distance square is 4 square meters.

d^{2}=(2\ \text{m})^{2}=4\ \text{m}^{2}

The received flux is luminosity over distance square

Dividing 16 watts by 4 square meters gives flux 4 watts per square meter.

F=\frac{16\ \text{W}}{4\ \text{m}^{2}}=4\ \text{W}/\text{m}^{2}