The inverse square law - Higher
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, A packet of energy of light and other forms of electromagnetic radiation. of light become spread over a wider area.
The relationship is not linear.
The light energy at twice the distance away is spread over four times the area.
The light energy at three times the distance away is spread over nine times the area, and so on.
For each distance of the plant from the lamp, light intensity will be proportional to the inverse of \(d^{2}\), \(d^{2}\) meaning distance squared.
Calculating \(\frac{1}{d^{2}}\):
For instance, for the lamp 10 cm away from the plant:
\(\frac{1}{d^{2}} = \frac{1}{10^{2}} = \frac{1}{100} = 0.01\)
If we refer back to the data the students collected from the experiment:
| Distance | Rate |
| 10 cm | 120 |
| 15 cm | 54 |
| 20 cm | 30 |
| 25 cm | 17 |
| 30 cm | 13 |
| Distance | 10 cm |
|---|---|
| Rate | 120 |
| Distance | 15 cm |
|---|---|
| Rate | 54 |
| Distance | 20 cm |
|---|---|
| Rate | 30 |
| Distance | 25 cm |
|---|---|
| Rate | 17 |
| Distance | 30 cm |
|---|---|
| Rate | 13 |
Completing the results table:
| Distance | \(\frac{1}{d^{2}}\) | Rate |
| 10 cm | 0.0100 | 120 |
| 15 cm | 0.0044 | 54 |
| 20 cm | 0.0025 | 30 |
| 25 cm | 0.0016 | 17 |
| 30 cm | 0.0011 | 13 |
| Distance | 10 cm |
|---|---|
| \(\frac{1}{d^{2}}\) | 0.0100 |
| Rate | 120 |
| Distance | 15 cm |
|---|---|
| \(\frac{1}{d^{2}}\) | 0.0044 |
| Rate | 54 |
| Distance | 20 cm |
|---|---|
| \(\frac{1}{d^{2}}\) | 0.0025 |
| Rate | 30 |
| Distance | 25 cm |
|---|---|
| \(\frac{1}{d^{2}}\) | 0.0016 |
| Rate | 17 |
| Distance | 30 cm |
|---|---|
| \(\frac{1}{d^{2}}\) | 0.0011 |
| Rate | 13 |
If we plot a graph of the rate of reaction over \(\frac{1}{d^{2}}\):
This 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.
