Physics Photo of the Week

April 4, 2008

Rainbow in the Valley - Photo by Miranda Hipple

Four weeks ago (March 4, 2008) we had a hard rainstorm in the late afternoon at Warren Wilson College.  Whe the rain cleared we were treated to a miraculous rainbow that Miranda Hipple captured on her cell phone camera.  Notice that the rainbow "ends" just beyond the WWC farm in the Swannanoa Valley.  We can also see the faint secondary bow to the right of the bright main rainbow.

The physics of the rainbow consists of sunlight entering a myriad of raindrops.  The light is refracted as it enters any raindrop, and dispersed into component colors both as it enters the raindrop and as it leaves the raindrop.  See the drawing below.

Only the raindrops which lie at an angle of 42 degrees ralative to the sunlight angle emit the "bow light" toward the observer.  The angle of 42 degrees is governed by the fact that raindrops are spherical and have a refractive index of about 1.33.  That means that the ratio of the speed of light in air is 1.33 times faster than it is in water.  The fainter secondary rainbow is caused by the light making two internal reflections in a raindrop.  Because with each partial internal reflection, a portion of the light is lost.  This makes the secondary rainbow much fainter than the primary bow as Miranda's photo shows.

Many of us have heard the myth that a "pot of gold" exists at the end of a rainbow, but no one ever has found this mysterious pot of gold.  The end of a rainbow, quite evident in Miranda's picture, proves to be quite elusive.  In fact the distance of a rainbow from an observer is impossible to define.  Any raindrops that are illuminated by the Sun and are located at the correct 42 degree angle from the Sun contribute light to the rainbow arch.  The distance of the raindrops from the observer does not matter.  That is why the "end" of the rainbow is so elusive.  Water droplets from a garden hose create rainbows right in front of our eyes.  Distant rain showers also create a rainbow.  One may say that the "location" of the rainbow itself is located at infinity.

Physics Photo of the Week is published weekly during the academic year on Fridays by the Warren Wilson College Physics Department.  These photos feature an interesting phenomena in the world around us.  Students, faculty, and others are invited to submit digital (or film) photographs for publication and explanation.  Atmospheric phenomena are especially welcome.  Please send any photos to dcollins@warren-wilson.edu.

All photos and discussions are copyright by Donald Collins or by the person credited for the photo and/or discussion.  These photos and discussions may be used for private individual use or educational use.  Any commercial use without written permission of the photoprovider is forbidden.

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