Interacting factors and the inverse square lawSpec 4.4.1.2
In short
Light intensity, carbon dioxide concentration and temperature interact, and any one of them may limit the rate of photosynthesis. On a graph, the factor on the x-axis is limiting where a curve rises. Light intensity follows the inverse square law: it is proportional to 1 ÷ distance², so doubling the distance gives one quarter of the intensity.
These factors interact, and any one of them may be the factor that limits photosynthesis. Which one is limiting can change with conditions, for example from the middle of a summer day to a winter morning.
To explain a graph with two or three factors, follow these steps:
- Look at the lines (or curves) for each set of conditions.
- Find the part where a curve is still rising. The factor on the x-axis is limiting there.
- Find the part where a curve is flat. A factor that is not on the x-axis is limiting there.
- If a line is higher because another factor was increased (for example a higher carbon dioxide concentration or temperature), that other factor was limiting the lower line.
- Where two lines are on top of each other, the factor on the x-axis is limiting both, so changing the other factor has no effect there.
To find the limiting factor, ask which factor would raise the rate if it were increased. That factor is the limiting one.
Light intensity and the inverse square law
Light intensity is inversely proportional to the square of the distance from the light source. This is the inverse square law. If you move a lamp twice as far away, the light intensity is one quarter as much, not one half.
Using the inverse square law
A lamp 10 cm from a plant gives a light intensity of 64 units. What is the light intensity when the lamp is moved to 40 cm?
- Distance has increased by a factor of 40 ÷ 10 = 4
- Light intensity falls by a factor of 4² = 16
- New intensity = 64 ÷ 16
Answer: 4 units
If light is the limiting factor, the rate of photosynthesis is roughly proportional to light intensity. So halving the distance gives four times the light intensity, and four times the rate (provided nothing else becomes limiting).
Limiting factors and greenhouses
Limiting factors are important in the economics of enhancing the conditions in greenhouses. Growers can add heat, light or carbon dioxide to gain the maximum rate of photosynthesis, so that plants grow faster and yield more.
But each addition costs money for fuel, electricity or carbon dioxide. The grower must still maintain a profit. It is only worth adding a factor if it is the limiting factor, and if the extra crop is worth more than the cost of adding it. Increasing a factor that is not limiting is a waste of money.
For an evaluation question, use data to compare the extra rate gained with the cost, and say whether the factor was actually limiting.
Written and checked against the AQA GCSE Combined Science (8464) specification · Updated October 2026