Specialised Optics of Rainbow Phenomena

Lunar rainbows, or moonbows, arise through the same refraction and internal reflection mechanisms that govern daytime arcs, yet they are triggered solely by moonlight. Because the intensity of lunar light is exceedingly faint, the human visual system relies almost exclusively on retinal rod cells, which govern scotopic vision. These photoreceptors cannot discriminate between wavelengths, leading observers to perceive moonbows as ghostly white bands across the night sky. In contrast, long-exposure photography accumulates sufficient photons to stimulate colour receptors on digital sensors, revealing the full spectral progression normally hidden from the naked human eye.

Ground-based observers typically witness rainbows as semicircular arcs because the Earth's surface obstructs the lower half of the optical cone. A rainbow is geometrically structured as a circle centred on the observer's antisolar point, situated precisely opposite the Sun. When an observer gains sufficient altitude, such as from an aircraft or an isolated mountain peak, the physical horizon recedes. Provided that airborne moisture exists both above and below the viewing plane, the full three-hundred-and-sixty-degree cone becomes visible. This complete circular formation demonstrates that the arc is not a fixed physical structure, but an observer-dependent optical cone.

The light emerging from a primary rainbow exhibits an exceptionally high degree of linear polarisation, often exceeding ninety percent. As incident rays enter a spherical water droplet, they strike the rear internal surface at an angle close to Brewster's angle for a water-air boundary. Under these specific geometric conditions, light waves vibrating parallel to the plane of incidence are largely transmitted out of the drop, whereas light vibrating perpendicular to this plane undergoes internal reflection. Consequently, the rays emerging towards an observer oscillate tangentially along the arc, causing the bow to vanish almost entirely when viewed through polarised sunglasses oriented perpendicularly.

While primary and secondary bows form away from the Sun, tertiary and quaternary rainbows require three and four internal reflections respectively, projecting their light back towards the solar direction. These higher-order arcs are remarkably difficult to observe in nature for two distinct optical reasons. First, each successive internal reflection within a raindrop causes substantial energy loss, drastically reducing the intensity of the exiting rays. Second, because these arcs surround the Sun rather than the antisolar point, their faint luminance is almost completely overwhelmed by intense solar glare. Consequently, capturing them demands sophisticated digital masking techniques to filter out direct sunlight.