A researcher at an agricultural laboratory investigates the photosynthetic efficiency of Chlorella vulgaris suspended in a bioreactor. To study the effect of light intensity on the rate of oxygen production, they position a high-intensity halogen lamp at varying distances, ddd, from the culture vessel. The relative light intensity, III, received by the bioreactor is inversely proportional to the square of the distance from the source, described by the inverse square law:
I∝1d2I \propto \frac{1}{d^2}I∝d21
Calculate the relative light intensity when the halogen lamp is placed at a distance d=25 cmd = 25\text{ cm}d=25 cm. Give your answer in standard form with the unit cm−2\text{cm}^{-2}cm−2.
When the distance ddd was decreased from 8 cm8\text{ cm}8 cm to 4 cm4\text{ cm}4 cm, the relative light intensity increased fourfold, yet the rate of oxygen production by the Chlorella remained constant. Explain why the rate of photosynthesis did not increase when the light intensity was increased in this range.