Light is an electromagnetic wave and therefore it follows the wave equation.
$\frac{\partial^2 \psi}{\partial t^2}= v^2 \frac{\partial^2 \psi}{\partial x^2}$
Now with some maths, the wave equation can be used with maxwell's equations to derive the speed of light:
$c=\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$
So the speed of any electromagnetic wave in a medium is same regardless of the wavelength. It only depends on the magnetic permeability and the electric permittivity of the medium. Then for example, in glass, why do speed of light differs with different colours?
I also remember a saying of Einstein in which he says that the speed of light is constant because it is made up of two constants. Therefore it doesn't change with changes in the reference frame. Now I cannot cite my claim about Einstein and it may be a mandela effect but I still need clarification on this also.
