Higher The Inverse Square Law and Light Intensity

Higher The Inverse Square Law and Light Intensity

Light intensity decreases with distance according to the inverse square law:

Intensity ∝ 1 / distance²

This means if you double the distance from the light source, the intensity falls to one quarter (not one half). If you treble the distance, intensity falls to one ninth.

Example calculation: A lamp produces an intensity of 400 arbitrary units at 10 cm. What is the intensity at 20 cm?

• Ratio of distances: 20/10 = 2
• Ratio of intensities: 1/2² = 1/4
• Intensity at 20 cm = 400 × 1/4 = 100 units

This is important for interpreting Elodea bubble-counting experiments. A graph of rate of photosynthesis against 1/d² (not against d itself) should give a straight line through the origin when light is the limiting factor, confirming the inverse square relationship.

Graph analysis at higher tier: On a graph of photosynthesis rate vs light intensity, the rate initially increases linearly. The gradient then decreases and the curve levels off — this plateau indicates that another factor (CO2 or temperature) has become limiting. The plateau itself shifts up when CO2 is increased or temperature is raised (up to the enzyme optimum), confirming which factor was limiting.