Q.How are rainbows formed?

Dispersion by a Prism – First Principles

Imagine a glass prism — a triangular block. You shine a narrow beam of white light into one face. What comes out the other side is not white. It is a beautiful band of colours: red, orange, yellow, green, blue, indigo, violet — the rainbow. That is dispersion.

Why does this happen? The short answer: different colours of light bend by different amounts when they enter and leave the prism. But the real question is why they bend differently.

The core idea: refractive index depends on colour

When light passes from air into glass, it slows down. The ratio of the speed of light in vacuum to its speed in the material is called the refractive index ($n$). For a given material, $n$ is not a single number — it changes with the colour (wavelength) of light.

Violet light has the shortest wavelength. It interacts more strongly with the glass molecules, so it slows down the most. That means violet has the highest refractive index in glass. Red light has the longest wavelength, slows down the least, and has the lowest refractive index.

Now, when light enters a prism at an angle, it bends according to Snell's law:

A larger $n_2$ (for violet) means a smaller $\sin\theta_2$ — so violet bends more toward the normal inside the prism. Red bends less. The same thing happens again when the light exits the other face. The net effect: each colour emerges at a slightly different angle.

The precise statement

Dispersion is the phenomenon in which the refractive index of a medium depends on the wavelength of light, causing different colours to deviate by different amounts when passing through a prism. White light, being a mixture of all visible wavelengths, is thus separated into its constituent colours.

The angle of deviation $\delta$ for a colour is given (for a thin prism of small angle $A$) by:

Since $n$ is different for each colour, $\delta$ is different. Violet deviates the most, red the least.

A mental picture

Think of a prism as a colour-sorting machine. White light enters as a single beam. Inside the glass, each colour travels at its own speed. Violet, the slowest, takes the sharpest turn. Red, the fastest, takes the gentlest turn. When they exit, they are no longer overlapping — they spread out into a fan of colours. …