A material's refractive index is highest for :

The refractive index ($\mathrm{\mu }$) of a medium for a given colour is defined as the ratio of the speed of light in air to the speed of light in that medium.

$\mathrm{\mu }=\frac{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{air}\left({\mathrm{v}}_{\mathrm{air}}\right)}{\mathrm{Speed} \mathrm{of} \mathrm{light} \mathrm{in} \mathrm{medium} \left({\mathrm{v}}_{\mathrm{medium}}\right)}$    ......(1)

The speed of light of a given colour can be expressed as the product of its wavelength and frequency.

${\mathrm{v}}_{\mathrm{air}}={\mathrm{\lambda }}_{\mathrm{air}}\mathrm{f}$        ....(2)

Because the frequency of light is independent of the medium, it does not change as it refracts.

$\therefore$${\mathrm{v}}_{\mathrm{medium}}={\mathrm{\lambda }}_{\mathrm{medium}}\mathrm{f}$                .....(3)

Substituting equations (2) and (3) in equation (1), we get,

$\mathrm{\mu }=\frac{{\mathrm{\lambda }}_{\mathrm{air}}}{{\mathrm{\lambda }}_{\mathrm{medium}}}$

$\mathrm{\mu }\propto \frac{1}{\mathrm{\lambda }}$

Medium's refractive index is inversely proportional to the wavelength of light.

Wavelength ($\lambda$) for violet light is the lowest. As a result, its refractive index must be the highest.