Tuesday, December 11, 2012

The Physics of Rainbows and Double Rainbows

by erics42, This post originally appeared at Function of a Rubber Duck.

Rainbow, Rainbow in the sky

A continuum of electromagnetic radiation streaking high
As I move, you move too
The angle between the sun, you, and me always 42

Often we think of rainbows as distinct bands of light. In actuality we are seeing every viewable wavelength of light i.e. a continuum. Electromagnetic radiation like light refract a.k.a. bend at different angles upon entering a new medium depending on their frequencies and the mediums refractive index. Different frequencies of light waves are responsible for the different colours we see in day to day life. Therefore, in rainbows, the different colours of light which inherently have different frequencies are refracted different amounts as they travel through and reflect off of rain drops. This causes the separation of the colours in the sky during a rainbow. Blue light for example has a higher frequency than red light and is bent at a greater angle back towards us as it passes through a rain drop making it appear lower in the rainbow than red light. Blue and all of the other frequencies of light are hitting all of the rain drops in the sky but the lower ones reflect with the right angle to bounce back to you! Cool eh?
But what is all this about different mediums and refractive indexes? Let me explain. Light travels 1.33 times slower in water than in space. This number is called the refractive index of light. It is written as n= c/v where n is the refractive index c is the speed of light in a vacuum and v is the speed of light in the new material. In comparison the refractive index of air is 1.0003. Therefore light travels 1.0003 times slower in air than in a vacuum (1.0003=c/v). To be technical light doesn’t actually slow down in terms of speed (that is constant) but has a decrease in velocity as it jiggles back and forth through the medium. The difference in the refractive indices of water and air cause the light to bend and reflect towards you at that angle of 42 degrees. Every point of light on the rainbow that you see forms approximately a 42 degree angle between the sun, the rain, and you. This is also what makes lenses work.
Did you know everyone sees a slightly different rainbow too? This is because of there dependance upon the angle between the viewer, sun, and rain. If I see a rainbow my friend a few miles away may also see a rainbow but it will be composed of different drops that satisfy the angle between the viewer, sun, and rain. This means you can never reach the end of the rainbow to find that a pot of gold. As you move towards the rainbow the rainbow you see will change too because of this law of angles.
What about double rainbows you say? What does it mean? Oh my, it’s so MAJESTIC! All the way across the sky! Sorry I’m getting carried away. What it technically means is that conditions are right for you to see light that has taken a slightly different path to you. The light coming from the outer and fainter rainbow has reflected off the inside of the rain drop twice instead of once which also causes the reversal of the orders of colour. As the light bounces off the inside of the rain drop not all of the light goes with it which causes this double reflection to be so much dimmer. Some light just passes straight through. Sunrise and late afternoons are the best times to view double rainbows because of the position of the sun in the sky and the amount of light that will follows this double reflection through the rain drop because of it. The second rainbow is in fact always there. It’s just not always visible. Look carefully for that second outer rainbow the next time you see an arc across the sky. In a way science is like that second rainbow. We don’t always see it right away, but if we take the time to look carefully we can see the unifying laws of nature all around us. An understanding of science only adds to the beauty of the world around us just like that of the second arc. When we understand the science we don’t only see and appreciate the aesthetic beauty of the rainbow but we can also appreciate how it works.

About this contributor: erics42 is a grade 10 student with a keen interest in physics and anything science. He watches Dr. Who- do you? His hobbies are creating strange edible food combinations and listening to all genres of interesting music.

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