Plants make their own food using photosynthesis. The food that plants produce is important, not only for the plants themselves, but for the other organisms that feed on the plants.

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.

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:

Distance | Rate |
---|---|

10 cm | 120 |

15 cm | 54 |

20 cm | 30 |

25 cm | 17 |

30 cm | 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 |

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.