Yes, there is a relationship between the volume of light (photons) and its traveling distance. This relationship is governed by the inverse square law, which states that the intensity or brightness of light decreases with the square of the distance from the source.
According to the inverse square law, if you double the distance from a light source, the intensity of the light at that new distance will be reduced to one-fourth (1/2^2) of its original value. Similarly, if you triple the distance, the intensity will be reduced to one-ninth (1/3^2), and so on.
The principle behind this relationship is based on the spreading of light as it travels outward from its source. As light spreads over a larger area as it moves away from the source, the same amount of light energy is distributed over a larger surface, resulting in a lower intensity or brightness.
It's important to note that the inverse square law applies to point sources of light, where the light is emitted from a single, concentrated location. In reality, light sources such as light bulbs or stars have finite sizes and may have other factors that affect their brightness at different distances. However, for practical purposes, the inverse square law is a useful approximation for understanding the relationship between light volume and traveling distance.