Final answer:
In a rainbow, the wavelength decreases and frequency increases from red to violet due to dispersion, illustrating their inverse relationship.
Step-by-step explanation:
As you move through the colors of the rainbow, the wavelength and frequency of the colors change due to dispersion. When white light is passed through a prism or refracted in water droplets to create a rainbow, the different colors are refracted to different extents based on their wavelengths. Red light has the longest wavelength and lowest frequency, and as you move through the spectrum to violet, the wavelength decreases while the frequency increases, due to their inverse relationship v = fλ, where v is the speed of light, f is the frequency, and λ is the wavelength. This is why violet light is bent the most in a prism and appears at the bottom of a rainbow, while red appears at the top.