Strathaven Academy Physics Department

The inverse square law describes how the intensity of a physical quantity radiating from a point source spreads out in space. For light, this quantity is irradiance, which is the power per unit area.

A point source is an idealized source of light that is treated as a single point in space, radiating energy uniformly in all directions. While no real object is a perfect point source, many can be approximated as one. For this approximation to be valid, the physical size of the source must be much smaller than the distance from the source to the observer. For example, a small light bulb can be treated as a point source in a room, and distant stars are considered point sources when viewed from Earth.

Imagine a point source of light with a constant power, $P$, measured in Watts (W). This light energy radiates outwards uniformly in all directions. As the light travels away from the source, it spreads out over the surface of an ever-expanding sphere.

The surface area of a sphere is given by the formula $A = 4\pi d^2$, where $d$ is the distance (radius) from the point source. The irradiance, $I$, is the total power of the source divided by the area over which it is spread: $$ I = \frac{P}{A} = \frac{P}{4\pi d^2} $$

Since the power of the source ($P$) and the term $4\pi$ are constants, we can group them into a single constant of proportionality, $k$. This shows that the irradiance is inversely proportional to the square of the distance from the source: $$ I = \frac{k}{d^2} \quad \text{or} \quad I \propto \frac{1}{d^2} $$

By plotting a graph of irradiance, $I$, on the y-axis against $1/d^2$ on the x-axis, we can verify this relationship. The equation $I = k/d^2$ can be compared to the equation of a straight line, $y = mx + c$. In this case, $y$ is $I$, $x$ is $1/d^2$, and the y-intercept $c$ is zero. This means the gradient of the line, $m$, is equal to the constant of proportionality, $k$.

This is the inverse square law. It means that if you double the distance from the source, the irradiance drops to one-quarter of its original value. If you triple the distance, it drops to one-ninth. This relationship is what you will investigate and verify in this experiment.