What is a Rainbow?

These photos were taken in front of my Dad's restaurant, Hidive, on the Embarcadero at Pier 28 1/2, San Francisco. 

Common knowledge of rainbows usually consists of the fact that they appear after it rains, they always have the same color pattern, and hopefully there is a pot of gold at the end. But if one tried to explain what a rainbow really is, in regards to Physics, what would they say?

Things We Need To Understand:

- Visible light is a very small section on the Electromagnetic Spectrum. 

- Every color is a representation of a different wave frequency (visible light is about 10^-6).

- Common knowledge of reflection and refraction of light.

- Dispersion happens when visible light passes through a triangular prism, and the visible light is separated into its different colors of red, orange, yellow, green, blue, and violet. 

 

After a nice mist of San Francisco rain, this rainbow appeared (at one point it was a double rainbow). What actually happened, that the physical eye does not allow us to see, was a series of refraction and reflection in the lingering water droplets in the air. Like we say in class, light does not just refract through water, but it also reflects light. Light waves refract when they cross over from one medium to another. Once the light is inside the water droplet, it reflects and then crosses from water back to air. This just means that light travels faster in air than it does inside a water droplet, therefore it slows down inside the water droplet so it can still maintain on the Path of Least Time. Every single frequency of the visible light spectrum (the colors of the rainbow) has a different wavelength, causing each light ray to reflect and refract in different directions. When light refracts for the second time through the series of water droplets, it's direction changes so it is coming towards observers on Earth. Because of this initial difference of wavelength, which causes the angles of refraction and reflection to vary, the final refracted ray of blue light will be slightly different then the location of the final refracted ray of red light. The overall amount of refraction between the incident light rays and the refracted rays directed to the observer's eyes is between 40 and 42 degrees due to different wavelengths. When theses light rays refract at such an angle, a rainbow is formed with its consistent order of red, orange, yellow, green, blue, and violet light.