A student carries out an experiment to verify the inverse square law for a point source of light - Scottish Highers Physics - Question 8 - 2023

Irradiance is the power per unit area incident on a surface, typically measured in watts per square meter (W/m²).

Using the recorded data:

• For each distance, calculate the product of the irradiance and the square of the distance,

  • At 0.200 m: $I imes d^2 = 142.0 imes (0.200)^2 = 5.68$
  • At 0.300 m: $I imes d^2 = 63.1 imes (0.300)^2 = 5.68$
  • At 0.400 m: $I imes d^2 = 35.5 imes (0.400)^2 = 5.68$
  • At 0.500 m: $I imes d^2 = 22.7 imes (0.500)^2 = 5.68$
  • At 0.600 m: $I imes d^2 = 15.8 imes (0.600)^2 = 5.69$

This shows that the product $I d^2$ remains approximately constant, indicating that:

d $I imes d^2 = constant$ Or conversely: I imes rac{1}{d^2} = constant

The irradiance decreases with increasing distance from a point source of light because as the distance increases, the same amount of light energy is spread over a larger area. According to the inverse square law, the intensity of light (irradiance) is inversely proportional to the square of the distance from the source, which means that if the distance doubles, the irradiance is reduced to a quarter of its original value. This results in a lower value of irradiance measured as you move away from the light source.