A Wavelength

The wavelength λ is the distance between the corresponding points of a wave in successive cycles.

Wavelength Range:

In studying how much energy an astronomical object gives off at various wavelengths. It sometimes is refered to a graph, or some equivalent representation, showing intensity as a function of wavelength (or frequency) as a spectrum. It is not really proper to talk about the energy given off at a particular wavelength.

For a specific wavelength to an arbitrary number of decimal places then even a small wavelength range has an infinite number of wavelengths. If there was even a little energy “at” each wavelength, then there would be an infinite amount of energy.

Instead, it is proper to talk about the energy given off over some wavelength (or frequency) range.

In this manner it worth to define the intensity function I(λ) such that I(λ) dλ is the energy per unit time per unit surface area given off by an object in the wavelength range λ to λ+ dλ. Similarly, I(ν) dν is the energy per unit time per unit surface area given off by an object in the frequency range ν to ν + dν.