The rainbow is an optical phenomenon characterized by the formation of colored bands in the sky. Even seen in an arc shape, its real shape is a circle.
The experiments and observations of René Descartes and Isaac Newton managed to give a scientific explanation for the phenomenon of colored lights appearing in the sky.
How are rainbows formed?
When the rays of polychromatic light (white light), coming from the Sun , enter the various water droplets suspended in the air, they undergo refraction and scatter into the seven colors characteristic of the rainbow . Chromatic dispersion is the physical phenomenon that explains the scattering of white light.
The mathematical relationship between the refractive index of a medium and the wavelength of electromagnetic radiation is inversely proportional, therefore, as each color of the electromagnetic spectrum has a characteristic wavelength, the refraction of each one of them is different. As a result, colors with longer wavelengths will undergo little change in their propagation direction, unlike colors with shorter wavelengths, which will suffer large deviations in their trajectories.
To observe a rainbow, the direction of propagation of the refracted light rays must reach the observer at angles close to 42°. As all light reaches the observer forming the same angle, the phenomenon will always be perceived in the form of an arc of circumference. However, the reality is that every rainbow has a circular shape, but the view of its entire circumference is impeded by the curvature of the Earth.