Scientific calculations - direct and inverse proportion - Higher
Direct proportion
As light intensity increases the rate of photosynthesis also increases. This is because photosynthesis is an energy requiring reaction, endothermic. More light energy will increase the rate at which oxygen is given off so more bubbles of oxygen will be produced per minute.
Inverse proportion
There is an inverse relationship between distance and light intensity - as the distance increases, light intensity decreases. This is because as the distance away from a light source increases, Visible electromagnetic radiation. becomes spread over a wider area.
Inverse square law
Light energy is proportional to the square of the distance of the light source from the plant.
The light energy at twice the distance away (2d) is spread over four times the area.
The light energy at three times the distance away (3d) is spread over nine times the area. So, the light intensity is inversely proportional to the square of the distance - this is the inverse square law.
For each distance of the plant from the lamp, light intensity will be proportional to \(\frac{1}{d^2}\).
If we refer to data students collected from an experiment:
| Distance of plant from light source in cm | Number of bubbles of oxygen produced per minute |
| 10 | 120 |
| 15 | 54 |
| 20 | 30 |
| 25 | 17 |
| 30 | 13 |
| Distance of plant from light source in cm | 10 |
|---|---|
| Number of bubbles of oxygen produced per minute | 120 |
| Distance of plant from light source in cm | 15 |
|---|---|
| Number of bubbles of oxygen produced per minute | 54 |
| Distance of plant from light source in cm | 20 |
|---|---|
| Number of bubbles of oxygen produced per minute | 30 |
| Distance of plant from light source in cm | 25 |
|---|---|
| Number of bubbles of oxygen produced per minute | 17 |
| Distance of plant from light source in cm | 30 |
|---|---|
| Number of bubbles of oxygen produced per minute | 13 |
Calculating \( \frac{1}{d^2}\):
For instance, for the lamp 10 cm away from the plant:
\( \frac{1}{d^2} = \frac{1}{10^2} = \frac{1}{100} = {0.01}\)
Completing the results table:
| Distance from light source in cm | \(\frac{1}{d^2}\) | Number of bubbles of oxygen produced per min |
| 10 | 0.01 | 120 |
| 15 | 0.004 | 54 |
| 20 | 0.0025 | 30 |
| 25 | 0.0016 | 17 |
| 30 | 0.001 | 13 |
| Distance from light source in cm | 10 |
|---|---|
| \(\frac{1}{d^2}\) | 0.01 |
| Number of bubbles of oxygen produced per min | 120 |
| Distance from light source in cm | 15 |
|---|---|
| \(\frac{1}{d^2}\) | 0.004 |
| Number of bubbles of oxygen produced per min | 54 |
| Distance from light source in cm | 20 |
|---|---|
| \(\frac{1}{d^2}\) | 0.0025 |
| Number of bubbles of oxygen produced per min | 30 |
| Distance from light source in cm | 25 |
|---|---|
| \(\frac{1}{d^2}\) | 0.0016 |
| Number of bubbles of oxygen produced per min | 17 |
| Distance from light source in cm | 30 |
|---|---|
| \(\frac{1}{d^2}\) | 0.001 |
| Number of bubbles of oxygen produced per min | 13 |
If we plot a graph of the rate of reaction over \(\frac{1}{d^2}\) :
The graph is linear.
The relationship between light intensity (at these low light intensities) is linear.
Be careful - the x-axis is values of \(\frac{1}{d^2}\). It is not of light intensity.
\(\frac{1}{d^2}\) is proportional to light intensity.