A rainbow is produced due to the phenomenon of dispersion of light, which is the splitting of white light into its component colors. This is caused by the refraction of light as it passes through raindrops in the atmosphere.

Dispersion occurs because different colors of light have different wavelengths. When white light enters a raindrop, it is refracted and partially reflected inside the drop. The different colors of light experience different angles of refraction and reflection, causing them to spread out or disperse.

As the dispersed light exits the raindrop, it goes through additional refraction and reflection. This causes the different colors to be redirected at different angles, resulting in the formation of a circular arc of colors in the sky, known as a rainbow.

The other options listed are not responsible for the formation of a rainbow. Interference of light refers to the interaction of two or more light waves, diffraction of light involves the bending of light waves around obstacles, and scattering of light by atmospheric dust refers to the redirection of light in different directions due to the presence of particles in the atmosphere.

Therefore, option 1: Dispersion of light, is the correct answer.