please prove the relation refractive index is inversely proportional to wavelength in a given medium

Refractive index n = c/v

where c is the velocity of light in vacuum.

v is the velocity of light in the medium.

v=fλ

where f is the frequency

λ is the wavelength.

substituting these values in the refractive index equation

n = c/fλ

Hence refractive index is inversely proportional to wavelength.