A rainbow in a glass of water is a beautiful demonstration that white sunlight is actually a mixture of all the colours of the visible spectrum. When light passes from air into glass or water (a denser medium), it slows down and bends — a process called refraction. Different colours (wavelengths) bend by slightly different amounts because the refractive index of glass and water varies with wavelength (dispersion), spreading the colours into a rainbow spectrum.
The same physics explains real rainbows in the sky: sunlight enters a spherical raindrop, refracts at the front surface, reflects off the back, and refracts again as it exits. Red light bends less than violet light, so the colours emerge at slightly different angles — red at about 42° and violet at about 40° from the antisolar point. The arc of a rainbow is always centred on the antisolar point, opposite the sun, and its radius matches the 40–42° range of the refraction angles.
Isaac Newton first systematically studied dispersion in 1666, passing sunlight through a prism to show that white light separates into a spectrum and that a second prism could recombine the colours back into white. This demonstrated that the prism does not create colours but merely separates pre-existing components. The concept of dispersion is fundamental to spectroscopy, fibre-optic communications, camera lens design (chromatic aberration), and astronomical instrumentation.
White sunlight contains all visible wavelengths from violet (~380 nm) to red (~700 nm). When light enters water, each wavelength bends by a slightly different amount because water's refractive index is slightly higher for shorter wavelengths (violet) than longer ones (red). This differential bending separates the colours, spreading them across the visible spectrum.
A rainbow appears as an arc (or full circle from an aircraft) because it is formed by all the raindrops that direct refracted and reflected light to your eye at the correct angle (40–42° from the antisolar point). All these drops lie on a cone centred on the antisolar direction, creating a circular arc at a constant angular radius around the point directly opposite the sun.
Yes! Shine a torch through a glass of water onto a white card, or use a garden hose to spray fine mist with the sun behind you. A glass prism splits light very clearly. On a sunny day, position a mirror in a bowl of water with sunlight shining on it; the reflected light forms a rainbow on the ceiling. These experiments all demonstrate refraction and dispersion.
Dispersion is the dependence of a medium's refractive index on the wavelength (frequency) of light. Because different colours travel at slightly different speeds in glass or water, a prism or raindrop separates them spatially. Dispersion is a problem in camera lenses (chromatic aberration) and in optical fibre telecommunications (pulses spread out over distance), but it is also exploited in spectrometers and gratings for precise wavelength measurement.
A primary rainbow (the bright inner bow) forms from a single internal reflection inside each raindrop, with red on the outside (~42°) and violet on the inside (~40°). A secondary rainbow (fainter, outer bow) forms from two internal reflections, reversing the colour order (violet outside, red inside) and appearing at ~51°. The region between the two bows (Alexander's dark band) is darker because no scattered light reaches the observer from that angular range.