Inverse Square Relationship between Distance and Brightness/Intensity

Inverse Square Law of Light Intensity

The inverse square law is a principal concept in physics which states that the intensity (or brightness) of light is inversely proportional to the square of the distance from the source of that light.

Essentially, if you double the distance of an object from a light source, the brightness of the light on the object decreases to a quarter of its original value.
This is because, as the distance from a light source increases, the light has to cover a larger area. Thus, the same amount of light is spread over a larger area, diluting its intensity or brightness.

The inverse square law is critically important in astronomy because it helps astronomers calculate properties like the distance or luminosity of a distant star or galaxy.
For example, by comparing the apparent brightness of a star (how bright it appears from Earth) with the star’s absolute brightness (how bright the star would appear if it were at a standard distance), astronomers can estimate the distance to that star.
This calculation is noteworthy in understanding the scale of the universe and the properties of galaxies and stars.

It’s crucial to understand the difference between brightness and luminosity in this context.
Brightness is the amount of light that an object emits per unit area.
Luminosity is the total amount of energy that a star or any other astronomical object radiates per unit time. It depends on both the size of the object and how hot it is.
Knowing the luminosity of an object and how far away it is, the apparent brightness can be calculated using the inverse square law.

The law can be applied using the formula: I = L / (4πd^2), where I is the intensity, L is the luminosity of the light source, and d is the distance from the source.
To find the distance, you can rearrange the formula to d = √(L/(4πI))
These calculations often require conversions between different units of measurements, so it’s vital to become familiar with the units used to measure distances and luminosities in astronomy. Common units include parsecs for distance and watts for luminosity.

In reality, the brightness of a star observed from Earth may be further reduced by dust and gas in space, which scatter and absorb some of the star’s light. This is known as interstellar extinction.