Inverse square law and light intensity

Drag the point along the curve

Distance from the lamp (in multiples of d): 3. Relative light intensity (1 = at d): 0.11

Drag the point. Stop at 2, then at 3, and read the height.

Predict, then check

Think about the pondweed investigation, with the lamp and a counted number of gas bubbles.

The pondweed is moved further from the lamp. What happens to the number of gas bubbles it produces in a set time?

What you need to know

• Light intensity is the amount of light reaching a given surface in a given period of time.
• It is one factor that limits the rate of photosynthesis, because light transfers the energy the reactions need.
• Light travels in straight lines from a source and spreads out, so the same light covers more area further away.
• Have a goYou walk backwards from a torch shining on a wall. The torch hasn't dimmed, but the patch of light looks fainter. Where did the light go?

  Nowhere. The same light is spread over a bigger area, so each bit gets less.

  Light spreads out as it travels, so further away the same light covers a greater area.

• The inverse square law: light intensity is inversely proportional to the square of the distance, so intensity ∝ 1/d².
• Double the distance and the light spreads over four times the area, so intensity falls to a quarter.
• Triple the distance and the intensity is one ninth of what it was.
• Have a goWhich fall is bigger: the drop in intensity from d to 2d, or the drop from 2d to 3d?

  d to 2d. Intensity goes from 1 down to ¼ (a drop of ¾), then only from ¼ down to 1/9.

  The curve is steep at first and then flattens, so the first doubling costs the most light.

• Watch the trap: doubling the distance does not halve the intensity, because the law uses distance squared.
• To calculate relative light intensity, work out 1/d² (d in cm in the pondweed investigation). It has no unit.
• Have a goA lamp is 5 cm from the plant. Work out the relative light intensity as 1/d².

  5 × 5 = 25, so the relative intensity is 1/25 = 0.04.

  Square the distance first, then take 1 over it. Using 1/5 would skip the squaring.

• In the investigation, you change light intensity by moving the plant, such as pondweed or algae, to different distances from the lamp.
• As the plant moves further from the lamp, light intensity and the rate of photosynthesis both fall.

The big picture

Light spreads out as it travels, so moving a plant away from a lamp spreads the same light over a bigger area. Light intensity follows the inverse square law, intensity ∝ 1/d²: double the distance and you get a quarter of the intensity, triple it and you get one ninth. In a photosynthesis investigation that means the rate falls as the plant moves away.

⚠ Watch out

Thinking doubling the distance halves the light intensity. The law uses the square of the distance, so doubling gives a quarter and tripling gives one ninth.

Memory hook

Double the distance, four times the area, a quarter of the light.

Check yourself

Say it out loud without looking: what happens to the area the light covers, and to the light intensity, when the distance from the lamp doubles? Then do the same for tripling.