What causes a rainbow to appear after rain?

A rainbow appears after rain due to the refraction, reflection, and dispersion of light in water droplets. When sunlight enters a water droplet, it slows down and bends (refracts) as it passes through the droplet. The light is then reflected off the inside surface of the droplet and exits at different angles, splitting into its various colors. The different wavelengths of light bend by varying amounts, creating the spectrum of colors that form the rainbow. The result is a circular arc of vibrant colors that can be seen when the Sun is behind you and the rain is in front.