Inverse-Square Law of Light

Lesson notes

Overview

Starlight spreads over a sphere, so brightness falls with the square of distance. This topic is rated advanced and is number 37 of 98 in Earth & Space. Deeper models, formal results and harder reasoning.

What you are seeing

The panel above shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

Light from a star spreads out over an expanding sphere, so the brightness (flux) at distance d is I = L/4πd². Doubling the distance makes it four times dimmer. If the true luminosity L of a star is known, from its type, measuring its apparent brightness gives its distance, which is the method of standard candles. The same law applies to any radiation from a point source, such as a lamp or a radio transmitter.

Reading the relationship

The expression "I = L/4πd²" is a compact summary of the idea. It uses the symbols I, L, π, d; name what each one stands for before you start. Notice that it contains a squared term, so doubling that quantity changes the result by a factor of four, and a ratio, so increasing the denominator makes the result smaller. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Set every slider to its middle value and note the shape of the curve. 2. Move one slider at a time and describe whether the curve shifts, stretches or turns. 3. Find the value where the behaviour changes sharply, then connect it to the formula.

Try this

Try to explain why the pattern holds, not just what it is. Look for limiting cases and what happens at the edges.

Common pitfalls

Earth and space systems work on very different scales of time and distance. Check which scale a number refers to before comparing it with another.

How it connects

It builds on “Stellar Lifetimes”, the topic before it in Earth & Space. Once you are comfortable, continue with “Parallax and Stellar Distance”.

Why it matters

Earth and space science helps us understand our planet, its climate and the wider universe.