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, photons of light become spread over a wider area.

An image showing the relationship between distance and light intensity.

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 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 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:

10 cm120
15 cm54
20 cm30
25 cm17
30 cm13

Completing the results table:

10 cm0.0100120
15 cm0.004454
20 cm0.002530
25 cm0.001617
30 cm0.001113

If we plot a graph of the rate of reaction over \(\frac{1}{d^{2}}\):

A graph showing the number of bubbles produced per minute.

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.