gen-define-the-inverse-square-law-for-lighting-and-give-one-shor-6f18

Define the inverse-square law for lighting and give one short worked example.

# Inverse-Square Law for Lighting **Definition:** The intensity of light is inversely proportional to the square of the distance from the source. $$I = \frac{P}{4\pi r^2} \quad \text{or simply} \quad I \propto \frac{1}{r^2}$$ Where: - *I* = intensity (illuminance) at distance *r* - *P* = power of the light source - *r* = distance from the source **In practical terms:** When you double the distance from a light source, the light intensity becomes 1/4 as bright. ## Worked Example **Problem:** A light meter reads 400 lux at 2 meters from a lamp. What is the illuminance at 4 meters? **Solution:** Using the inverse-square relationship: $$\frac{I_2}{I_1} = \frac{r_1^2}{r_2^2}$$ $$I_2 = I_1 \times \frac{r_1^2}{r_2^2} = 400 \times \frac{2^2}{4^2} = 400 \times \frac{4}{16} = 400 \times \frac{1}{4} = 100 \text{ lux}$$ **Answer:** The illuminance at 4 meters is **100 lux** (one-quarter of the original intensity).