Light Intensity Falls With Distance

1. Light from a lamp spreads over a larger area as distance increases, so the energy received per unit area decreases.
2. The inverse square law states that light intensity is inversely proportional to the square of the distance from the source.
3. The relationship is ** $$I\propto \frac{1}{d^2}$$ **, where $I$ is light intensity and $d$ is distance.
4. For relative light intensity, use ** $$I=\frac{1}{d^2}$$ ** when no constant of proportionality is supplied.

Distance Changes Intensity by a Square

1. If distance is multiplied by a scale factor $n$, light intensity is divided by $n^2$.
2. Doubling distance gives ** $$\frac{1}{2^2}=\frac{1}{4}$$ ** of the original intensity.
3. Tripling distance gives ** $$\frac{1}{3^2}=\frac{1}{9}$$ ** of the original intensity.
4. Halving distance gives ** $$\frac{1}{(1/2{)}^2}=4$$ ** times the original intensity.

Calculate Relative Light Intensity

1. Convert all distances to the same unit before squaring them.
2. At $d=0.20\mathrm{m}$, ** $$I=\frac{1}{(0.20{)}^2}=25{\mathrm{m}}^{-2}$$ ** as a relative value.
3. At $d=0.40\mathrm{m}$, ** $$I=\frac{1}{(0.40{)}^2}=6.25{\mathrm{m}}^{-2}$$ **.
4. The second value is one quarter of the first because the distance doubled.

Link Intensity to Photosynthesis

1. When light is the limiting factor, the rate of photosynthesis is directly proportional to light intensity.
2. Moving a lamp closer increases light intensity, so chlorophyll absorbs more energy and the rate increases.
3. The rate does not keep increasing indefinitely because carbon dioxide concentration or temperature can become limiting.
4. A graph of rate against $1/d^2$ tests the relationship more directly than a graph of rate against $d$.

Check the Calculation

1. A larger distance must give a smaller relative intensity, so use this pattern to check your answer.
2. Keep the same distance unit throughout a comparison because changing units changes the numerical relative intensity.