The mathematical relationship between wavelength and intensity of light depends on the specific context and the phenomenon being considered. In general, the intensity of light refers to the amount of power per unit area carried by the light wave.
If we assume a monochromatic light source (a single wavelength), the intensity of light can be described by the inverse square law. According to this law, the intensity of light decreases with the square of the distance from the source.
However, if we consider the interaction of light with a medium or an object, the relationship between wavelength and intensity can vary. For example, in the context of absorption or scattering of light by a medium, the intensity of light may decrease or be modified differently depending on the wavelength.
Additionally, in some situations, the intensity of light may be related to the energy of individual photons, which is determined by their frequency (or equivalently, wavelength). This relationship is described by Planck's law and the photoelectric effect.
In summary, the relationship between wavelength and intensity of light can vary depending on the specific phenomenon being considered, and it is important to consider the context and physical principles at play.