Justify why the brewster angle for a transparent medium is different for different colours of lights?

Hint: Brewster's angle (sometimes called the polarisation angle) is the angle of incidence at which light of a specific polarisation is completely transmitted through a clear dielectric surface with no reflection. When unpolarized light strikes the surface at this angle, the light that is reflected is completely polarised. Sir David Brewster (1781–1868), a Scottish scientist, was the inspiration for this unique angle of incidence.

Complete step by step answer:
Some light is reflected when it comes into contact with a border between two media with different refractive indices, as indicated in the diagram above. The Fresnel equations explain the proportion of light that is reflected and are dependent on the polarisation and angle of incidence of the entering light. If the angle of incidence is less than 45 degrees, the Fresnel equations indicate that light with p polarisation (electric field polarised in the same plane as the incident ray and the surface normal at the point of incidence) will not be reflected
\[{\theta _{\text{B}}} = \arctan \left( {\frac{{{n_2}}}{{{n_1}}}} \right)\]
where${n_1}$is the refractive index of the original medium (the "incidental medium") through which light propagates, and${n_2}$is the index of the other medium. Brewster's law is the equation that defines the angle, and Brewster's angle is the angle described by it.
The tangent of the polarising angle of incidence to the clear medium is equal to the refractive index of the medium, according to Brewster's law \[\left( {\tan {i_p} = mu} \right)\]
The angle is determined by the medium's refractive index.
The angle of polarisation ${i_p}$ will change with regard to the colour of the light.
Because the refractive index of the medium is a function of the wavelength of incoming light, the angle of polarisation ${i_p}$ will change depending on the colour of the light.

Note:
The reflection of p-polarized light is lower than that of s-polarized light across a wide range of angles around Brewster's angle. As a result, reflected light is highly s-polarized when the sun is low in the sky. Polarizing sunglasses filter horizontally polarised light, preferring to prevent reflections from horizontal surfaces, which is a frequent source of glare, using a polarising material such as Polaroid sheets. The effect is strongest on flat surfaces like water, but it also reduces reflections from highways and the ground.