If light gets broken up into its constituent colours because of difference in wavelengths, then why do all electromagnetic waves like microwaves, x-rays have same speed in a medium, although they hve different wavelengths?

Dear Student,

The speed of a wave is a product of its wavelength and frequency.Since, a wave with shorter wavelength has higher frequency and their product is constant and same for all different types of waves in an electromagnetic wave. Hence, it does not splits into different constituent.

Regards