Light intensity and the inverse square lawHigher tier
Light does not get weaker steadily as you move away from a lamp — it drops off much faster than that. Light intensity is inversely proportional to the square of the distance: intensity ∝ 1 ÷ d². Move twice as far away and the light is a quarter as intense, not half.
How to do it — step by step
- Measure the distance d from the lamp to the pondweed, keeping every distance in the same unit.
- Square it: d × d.
- Light intensity ∝ 1 ÷ d², so work out 1 ÷ d² — that number is your measure of the light intensity.
- To compare two distances, the intensity changes by a factor of (old d ÷ new d)².
Worked example
At 20 cm: 1 ÷ 20² = 1 ÷ 400 = 0.0025
0.0025 ÷ 0.01 = 0.25 — the light is a quarter as intense
Doubling the distance did not halve the light. It quartered it. That is the whole point of the word square in the inverse square law.
Why you plot 1 ÷ d² and not the distance
In the photosynthesis required practical (required practical 6 in separate Biology, required practical 5 in Combined Science) you move a lamp to different distances from a piece of pondweed and count the bubbles of oxygen given off.
The problem is that you have no light meter — you cannot measure the intensity directly. What you can measure is the distance. So you use 1 ÷ d² as a stand-in for the light intensity, because it is proportional to it. Plot rate of photosynthesis against 1 ÷ d² and you get a sensible relationship; plot it against distance and you get a curve that is much harder to interpret, because distance and intensity are not proportional.
The 1 ÷ d² values have no useful unit of their own, so they are usually described as arbitrary units. That is fine — you are only using them to compare one distance with another.
Mistakes that cost marks
- Forgetting to square. Using 1 ÷ d instead of 1 ÷ d² is the single most common error.
- Assuming it is proportional. Half the distance does not mean double the light — it means four times the light.
- Mixing units. If one distance is in cm and another in m, every comparison is wrong. Convert first.
- Plotting against distance. If the question asks you to show the relationship, the x-axis should be 1 ÷ d².
- Rounding too early. 1 ÷ d² values are small — keep the decimal places until the final answer.
Now practise it — free
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