A2 Biology 9700: Investigating Light Intensity as a Limiting Factor

A student investigates the effect of light intensity on the rate of photosynthesis in a sprig of the aquatic plant Cabomba. The cut end of the shoot is held underwater in a beaker of sodium hydrogencarbonate solution (as a source of dissolved carbon dioxide), and a lamp is placed at various distances from the plant. At each distance, once the rate of bubbling has become steady, the student counts the number of oxygen bubbles released from the cut stem in one minute and uses this as a measure of the rate of photosynthesis. Light intensity reaching the plant is inversely proportional to the square of the distance between the lamp and the plant. The student intends to keep temperature constant throughout.

(a) The lamp is placed 10 cm from the plant, and later moved to 40 cm from the plant. Calculate the light intensity reaching the plant at 40 cm as a fraction of the light intensity reaching the plant at 10 cm. Show your working. [3]

(b) The student plans to plot a graph of the number of bubbles produced per minute against distance from the lamp. Explain why plotting the number of bubbles produced per minute against $\dfrac{1}{(\text{distance})^2}$ instead would be expected to give a more linear relationship, assuming light intensity is the limiting factor throughout. [2]

(c) The student increases light intensity simply by moving the lamp closer to the plant, without taking any other precautions. Identify one variable, other than light intensity, that is not adequately controlled by this method, and explain how it could make the results of the investigation misleading. [3]

Part (a): Applying the inverse square law

Light intensity, $I$ , is inversely proportional to the square of the distance, $d$ , from a point source of light:

$I \propto \frac{1}{d^2}$

Comparing the light intensity at 40 cm with the light intensity at 10 cm:

$\frac{I_{40}}{I_{10}} = \frac{d_{10}^2}{d_{40}^2} = \frac{10^2}{40^2} = \frac{100}{1600} = \frac{1}{16}$

So the light intensity reaching the plant at 40 cm is $\frac{1}{16}$ of the light intensity reaching it at 10 cm. That is, 0.0625, or 6.25%, of the original intensity.

Part (b): Why plotting against 1/distance² gives a straighter line

Assuming light is the limiting factor throughout the investigation, the rate of photosynthesis (measured here as bubbles produced per minute) rises in direct proportion to light intensity. Since light intensity itself is proportional to $\frac{1}{(\text{distance})^2}$ rather than to distance, the rate is also expected to be proportional to $\frac{1}{(\text{distance})^2}$ .

A graph of rate against distance would therefore be a curve (rate falls steeply at first as distance increases, then levels off), because the relationship between rate and distance is not a simple proportional one. Plotting rate against $\frac{1}{(\text{distance})^2}$ instead converts the relationship into a directly proportional one, which should give points lying close to a straight line through the origin if light really is the limiting factor throughout, making it much easier to check this assumption and to identify any point where the results deviate from the expected straight line (which would suggest light has stopped being the limiting factor).

Part (c): An uncontrolled variable, temperature

Moving the lamp physically closer to the plant to raise light intensity also brings the plant closer to the lamp’s source of heat. This is very likely to raise the temperature of the water surrounding the plant, especially at the closest distances.

Because the Calvin cycle depends on enzymes such as rubisco, whose rate of activity is sensitive to temperature, an unintended rise in temperature at short distances could itself change the rate of photosynthesis, independently of the increase in light intensity, for example, by speeding up enzyme activity (if still below the optimum temperature) or slowing it down through denaturation (if temperatures become too high). This means any observed increase (or eventual decrease) in bubble count as the lamp is moved closer cannot be confidently attributed to light intensity alone, since temperature has changed at the same time. To control for this, a heat-absorbing water bath (“heat shield”), such as a glass tank of water, could be placed between the lamp and the beaker to absorb heat while still allowing light through.

Final answers

(a) Light intensity at 40 cm is $\frac{1}{16}$ (0.0625, 6.25%) of the light intensity at 10 cm.
(b) Rate is expected to be proportional to $\frac{1}{(\text{distance})^2}$ (since light intensity is), so plotting against this quantity, rather than distance itself, should give a straight line through the origin, making deviations easier to detect.
(c) Temperature is not controlled. Moving the lamp closer also increases heat reaching the water, which can itself affect the (temperature-sensitive) enzyme-catalysed Calvin cycle reactions, confounding the effect of light intensity; a heat-absorbing water bath could control this.