A First Course in Physics · Ch. XIX, §§ 502–505 · Chapter 19: Nature and Propagation of Light
59. How bright? The inverse square law and photometers
Goal: Your student can explain why illumination falls off as the square of the distance, and compare two lights with a grease-spot (Bunsen) photometer.
You'll need
- The book, open to these pages
- A sheet of plain white paper and a little cooking oil or butter (for a grease spot)
- Two flashlights or two lamps, or one bulb and a candle (with an adult)
- A tape measure
- A notebook and pencil
- A calculator (optional, for the problems)
What's in the book
Light spreads over four times the area at twice the distance (the inverse square law); Rumford's shadow photometer; candle power; Bunsen's grease-spot photometer. Five problems follow.
The lesson, step by step
Hook question
SayIf you move a reading lamp twice as far from your book, does the page get half as bright?
Read together
Read §§ 502–505. The law:
the intensity of the illumination due to a given point source must vary inversely as the square of the distance from the source.
Try it: a grease-spot photometer
Rub a drop of oil into the middle of the paper. Hold it up between two lights in a dark room and look at it from one side: the spot looks dark when that side is brighter, light when it is dimmer. Slide the paper until the spot almost vanishes: the illumination is equal on both sides (§ 505). Measure the two distances. The stronger light is stronger by the square of the ratio of the distances.
Explain the idea
Light from a point spreads out like a growing sphere. At twice the distance the same light covers four times the area, so each square foot gets one fourth as much (Fig. 411). The same law held for sound (§ 449) and for gravity (§ 31).
What we know now: "candle power" is now the candela, and the total light from a bulb is given in lumens; an ordinary LED bulb is about 800 lumens.
Say it back
Your student explains how the shadow photometer in Fig. 412 compares a gas flame with candles.
Problems
Work problems 1–5 on book page 395.
Afterwards
Read the lumens on a few light bulb boxes and compare them with the watts.
Tip
Keep candles on a saucer away from paper and curtains, and have an adult present.
Answers to the book's problems
1. 1.5 m. 2. About 415 candle power (32 × (36/10)²). 3. About 0.58 m from the 5-candle-power light (1.42 m from the other). 4. About 147,000 times as strong ((92,000,000/240,000)²). 5. 36 candle power.
Worked out for this site from the scan. If a number in your copy differs, trust the book.