A Rainbow in Narada Falls

A Rainbow in Narada Falls
-Photo by Matthew T. Ross-

I recently took a trip to Mt. Rainier National Park. Aside from getting to see a magnificent view of the mountain for which the park is named, my friends and myself got to spend some time at the stunning Narada Falls. I hope the image is able to do the fall justice because it really was a spectacular view. In the future I might write an article on the flow of water as it careens off a cliff, but for now I wanted to focus on the physics of light as it passes through the mist created by the waterfall.

We start with a plume of water droplets flying into the air as the result of their leap off of a precipice into a pile of rocks below. This violent act is what sets the stage for the light show about to take place. Light hits the droplets of water that bounce off the rocks below the waterfall. Some of this light is simply reflected off the surface of the water droplet and gets collected by our retinas. Some of the light, however, enters the droplet of water where it is refracted. Refraction refers to the way waves alter their direction as the result of passing from one medium to another. In this case the light passes from the air into the water. Once the refracted light hits the back of the water droplet some of the water just keeps on traveling out the back, while some of it gets reflected and starts heading back towards the "front" of the droplet. The reflected light is then refracted once more as it passes from the water medium back into the air. The key here is that the angle to which the light is refracted depends on the wavelength of light. The lower frequency waves are refracted less than the high frequency waves. Our eyes detect different wavelengths of light which we perceive as different colors (low frequency is red and high frequency is violet). What this means is that by refracting the light you are separating the individual wavelengths. This property is called dispersion. The greatest intensity light is found at 42°.

Diagram by KES47. Source. Public Domain

The above diagram summarizes everything explained above. Notice how the difference in the angle of separation between the different wavelengths of light increases at it is refracted. 

For those familiar with "The Hitchhiker's Guide to the Galaxy" by Douglas Adams the number 42 might seem familiar as "the answer to the ultimate question of life, the universe and everything." Some fans of the books have proposed that Douglas Adams got the number from the physics behind the formation of rainbows. Alas, however, Adams himself has denied this claim saying "I sat at my desk, stared into the garden and thought '42 will do'. I typed it out. End of story."