Inverse Square for Lamps (Physics)

Lesson notes

Overview

Doubling the distance from a lamp quarters the illumination. This topic is rated intermediate and is number 174 of 227 in Physics. Builds on the basics with relationships, methods and trade-offs.

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

The illumination on a surface from a point source is E = I/d², where I is the luminous intensity and d the distance. Doubling the distance quarters the brightness because the same light spreads over four times the area. This explains why a reading lamp should be close to the page, why theatre lights must be powerful when they are far away, and how photographers use the light fall-off to separate a subject from the background.

Reading the relationship

The expression "E = I/d²" is a compact summary of the idea. It uses the symbols E, I, 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

Predict the outcome first, then test extreme slider values to find where the pattern changes or breaks.

Common pitfalls

Check units and directions first. Many mistakes come from mixing up a scalar with a vector, or from using a formula outside the conditions where it holds.

How it connects

It builds on “Fresnel Reflection at Normal Incidence”, the topic before it in Physics. Once you are comfortable, continue with “Inverse Square Law for Radiation Safety”.

Why it matters

Physics explains how the world moves, heats, shines and interacts, and the same principles power technology around you.

Where you might use it

Revising “Inverse Square for Lamps” before a class, exam or certification
Designing vehicles, bridges and devices where motion, forces or waves must be predicted
Understanding how sensors, lasers and communication links actually work
Explaining everyday phenomena such as sound, light, heat and orbits

Frequently asked questions

What is Inverse Square for Lamps?

Doubling the distance from a lamp quarters the illumination. It is an intermediate topic in Physics.

How do I use the Inverse Square for Lamps simulation?

The panel at the top shows a graph of the function. Each slider changes one parameter, so you can see exactly how the curve bends, shifts or stretches. Move the sliders one at a time, then press Space to pause the animation and look closer.

What does the formula mean?

The expression E = I/d² packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.

Who is this topic for?

Builds on the basics with relationships, methods and trade-offs. If the quiz feels hard, reread the lesson notes and try the previous topic first.

What should I learn before this?

Start with “Fresnel Reflection at Normal Incidence”, the previous topic in Physics. Each topic in a subject builds on the ones before it.

How do I track my progress?

Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.