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 defined as the power per unit area incident on a surface, typically measured in watts per square meter (W/m²). It quantifies the intensity of light hitting a given area.

Using the recorded data, we can establish the inverse square relationship between irradiance (I) and distance (d) as follows:

1. Calculate the product of irradiance and the square of the distance for each data point:

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

2. Notice that the product remains constant, verifying the relationship as: $I imes d^2 = constant$ or I = rac{constant}{d^2}.

The irradiance decreases with increasing distance from a point source of light due to the geometrical spreading of light. As the distance increases, the same amount of light energy is distributed over a larger area. The inverse square law explains this phenomenon, where the intensity of light (irradiance) is inversely proportional to the square of the distance from the source. Therefore, as distance (d) increases, the irradiance (I) decreases according to the formula: I = rac{P}{4 ext{π}d^2} where P represents the total power emitted by the light source.