A rainbow appears semicircular and of consistent size due to the interaction of sunlight with water droplets in the air, combined with the observer’s viewpoint.

Position of the Sun: The sun must be positioned behind the observer for a rainbow to be visible. The light from the sun enters water droplets in the air, which act as tiny prisms.

Position of Water Droplets: Water droplets in the atmosphere are roughly spherical. As sunlight enters each droplet, it undergoes refraction (bending), dispersion (separating into colors), internal reflection, and then refraction again as it exits. This dispersion splits the white light into a spectrum of colors.

Process of Dispersion: When light enters the droplet, shorter wavelengths (like blue and violet) bend more than longer wavelengths (like red). This creates a color separation. After internal reflection inside the droplet, the light exits and bends again, forming a spectrum.

Semicircular Shape: The rainbow appears semicircular because the droplets refract light at a specific angle (about 42 degrees for red light and slightly less for blue light) relative to the incoming sunlight. 

From the observer’s perspective, only droplets positioned at this angle from the line of sight reflect light into their eyes, forming a circular arc. Since the ground obstructs the lower part, we usually see only a semicircle.

Consistent Size: The size of the rainbow remains consistent because the 42-degree angle is fixed; thus, a rainbow appears roughly the same size no matter where or when it is observed.