Plants make their own food using photosynthesis. The food is important for the plants and for organisms that feed on the plants. Optimum rates of photosynthesis produce maximum plant yields.

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.

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 (d^{2}).

Calculating 1/d^{2}:

For instance, for the lamp 10 cm away from the plant:

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

Distance from light source (cm) | Rate of photosynthesis (bubble per min) |
---|---|

10 | 120 |

15 | 54 |

20 | 30 |

25 | 17 |

30 | 13 |

Completing the results table:

Distance from light source (cm) | 1/d squared | Rate of photosynthesis (bubble per min) |
---|---|---|

10 | 0.0100 | 120 |

15 | 0.0044 | 54 |

20 | 0.0025 | 30 |

25 | 0.0016 | 17 |

30 | 0.0011 | 13 |

If we plot a graph of the rate of reaction over 1/d^{2}:

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/d^{2}. It is not of light intensity.

1/d^{2} is *proportional* to light intensity.