# Scientific calculations – 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, 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 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 a lamp 10 cm away from the plant:

If we refer back to the data the students collected from the experiment:

Distance from light source in cmNumber of bubbles produced per minute
10120
1554
2030
2517
3013

Completing the results table:

Distance from light source in cm1/d squaredNumber of bubbles produced per minute
100.0100120
150.004454
200.002530
250.001617
300.001113

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

The graph is linear.

The relationship between light intensity - at these low light intensities – 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.