Rainbows and Rays
- Author:
- Anson Ho
This simulation shows how a rainbow is formed from the perspective of geometric optics, specifically the Descartes and Newton theories. These make the assumptions that (1) raindrops are spherical and (2) droplet size doesn't matter.
The only variable here is the vertical displacement of the incident ray, expressed as a decimal fraction of the drop radius - this is known as the impact parameter and ranges from 0 to 1 in magnitude, where negative values represent impingement on the bottom half of the drop. This can be adjusted using the slider in the applet.
Due to the wavelength dependence of refractive index, white light from the Sun disperses into a spectrum of colours. A single internal reflection forms what is known as the primary bow, whereas two internal reflections forms the secondary bow. Note that these are not total internal reflections, else the light would be trapped inside the drops forever.
The option is provided to show refraction out of the droplet at the 1st internal reflection point. This highlights the question of why the rainbow needs internal reflections to be formed, and can be understood in terms of maximum/minimum points.
The user can also change the refractive index of water and the spread of colours. It should be noted that this amount of spread may not necessarily be representative of a real rainbow, but is nevertheless useful as a visual aid. Note also that when the refractive index n is set to 1, the simulation shows not white light (as it should) but still some dispersion.