Scientific calculations - Higher

There is an inverse square relationship between distance and light intensity – as the distance increases, light intensity decreases, but this is not a linear relationship.

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 the distance squared (d2).

Calculating 1/d2:

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 from light source (cm)Rate of photosynthesis (bubble per min)
10120
1554
2030
2517
3013

Completing the results table:

Distance from light source (cm)1/d squaredRate of photosynthesis (bubble per min)
100.0100120
150.004454
200.002530
250.001617
300.001113
A graph showing the number of bubbles produced per minute.

If we plot a graph of the rate of reaction over 1/d2:

The graph is linear.

The relationship between light intensity and the inverse square of the distance is linear.

Be careful – the x-axis is values of 1/d2. It is not of light intensity.

1/d2 is proportional to light intensity.

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