Dispersion

The refractive index of a material depends on the wavelength of light (dispersion). It is largest for violet (shortest wavelength) and smallest for red (longest wavelength), as in Cauchy's relation $\mu\approx A+\dfrac{B}{\lambda^2}$, so $\mu_v>\mu_r$.

The focal length of a lens is given by $\dfrac1f=(\mu-1)\left(\dfrac1{R_1}-\dfrac1{R_2}\right)$. Since $\mu$ is larger for violet, its focal length is shorter: $f_v<f_r$. A violet ray is bent more than a red ray, so the lens focuses the colours at different points. This gives coloured fringes around images, called chromatic aberration.

In the morning and evening the Sun's rays enter the atmosphere obliquely and travel a much longer path through air than at noon. Along this long path, dust and air molecules scatter and absorb a large part of the light, especially the short wavelengths (scattering $\propto 1/\lambda^4$). The light reaching the eye is therefore weaker in intensity and reddish, so the Sun looks less bright, even though its distance from us is almost the same.

The refractive index of glass is greater for violet than for red, so a prism deviates violet light the most and red light the least. The prism bends all rays towards its base. Violet, deviated more, ends up closer to the base (the bottom of the spectrum) and red, deviated least, remains farthest from the base (the top). This is the case when the prism rests with its base down.

(d) violet light

Refractive index increases as wavelength decreases (Cauchy's relation $n=A+B/\lambda^2$). Violet has the shortest wavelength of the visible colours, so it has the greatest refractive index, and it is bent the most.

(c) dispersion and total internal reflection

Sunlight entering a spherical water droplet is first refracted and dispersed into its component colours (since the refractive index differs with wavelength), then undergoes total internal reflection at the inner back surface of the droplet, and is finally refracted again as it leaves — producing the rainbow.