Scientific calculations - distance and light intensity - Higher only
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 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.
The light intensity is A relationship between two variables where as one variable increases, the other variable decreases, eg as the volume doubled, the pressure decreased by half. 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 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 \(\frac{1}{d^{2}}\):
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.