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IntroductionEdit

Place a prism by your window on a nice afternoon. What do you see? A rainbow? Let's explore why this happens.

                        Prism rainbow schema

When polychromatic light, or white light, passes through a prism, it is separated into its different component colors. This is due to a phenomenon called dispersion. The word itself comes from the way in which a prism "disperses" light. Dispersion happens because the speed of light in a prism changes, and each color in the prism has its own individual speed. Let's break it down.

The Experiment Edit

Although it may be hard to see with the naked eye, white light is not simply a homogeneous entity. It was Sir Isaac Newton that made the revoluntionary discovery that in fact, white light is composed of different colors. In his experiment, he constructed an prism apparatus consisting of two prisms to demonstrate the separation of white light. He passed white light at the first prism, and then directed the separated color rays, or the oblong spectrum of colors--red, yellow, green, blue and violet, back at the second prism to produce back white light. An old theory suggested that all rays of white light striking a prism would be equally refracted. However, Newton argued that white light is really a mixture of many different types of rays, that the different types of rays are refracted at slightly different angles, and that each different type of ray is responsible for producing a given spectral color.

RefractionEdit

In order for dispersion to happen, light rays that enter the prism must undergo refraction, which is defined as the bending of a light ray as it travels from one medium to another. In the case of dispersion in the prism, light rays travels from the air and into the prism, thus, experiencing refraction.


Absolute Index of RefractionEdit

The diagram above indicates that red light travels the fastest because it has the largest index of refraction, which measures how much the wavelength of the light is bent as it passes through a medium. The equation for the absolute index of refraction is represented by:

n=c\v

The formula asserts that the absolute index of refraction of a medium, n, is the ratio of the speed of light, c, which is 3.00 x 108, to the speed of light in the new medium, v. The index of refraction for any medium must be greater than 1. In addition, an important relationship to note is that the greater the refracted angle, the less bending of light there is resulting in a slower speed of light in a medium. The higher the index of refraction, the more light can be dispersed in that material.

                               Phys3

The table above notes the absolute indices of refraction for several common mediums,. As indicated, each material has a different refractive index. Each color has its own distinguished wavelength. When light travels from one material to another, such as from air to glass, the difference in the indices of refraction causes the light to bend. The refracted angles for the light rays are different depending on the different wavelengths of light. In the case of the prism, when white light is directed through the two sides, different wavelengths the component colors in the visible light spectrum will bend varying amounts when it passes through the prism. Therefore, the dispersion of colors results in the appearance of a rainbow as the white light leaves the prism.


RainbowsEdit

Dispersion is actually quite a common phenomenon in nature.

                  Rainbow-1

Similar to when white light is passed through a prism to form a spectrum of colors, a rainbow is a spectrum formed when sunlight passes through water droplets in the atmosphere. The droplets almost act as tiny prisms because rays of sunlight is being dispersed in the droplets to form the spectrum. Sunlight is refracted when it passes the water droplets, or rain. Each color is refracted at different angles, and the light rays eventually experience a total internal refraction, which means that light is also reflected as a result. When it is reflected, it is once again refracted and dispersed, as demonstrated in the image below.

                  Rainbow-raindrop 

Imagine this as a raindrop. When sunlight passes from air into the rain drop, the the component colors experience speed changes due to the differences in their frquencies. As seen in the image above, sunlight is refracted once when it enters the raindrop. Then, it is reflected once on the opposite end of the raindrop, although some light does pass through back out into the air. However, the rest is reflected backwards and due to another occurance of refraction, it bends again before it ultimately leaves the raindrop.

Basic OpticsEdit

Each droplet may produce an entire light spectrum upon contact with sunlight, however, one may be inclined to ask, then why do we see wide bands of colors in a rainbow? It is as if different areas disperse different single colors. That is not the case. Here's why.

                  Rainbow-spectrum

According to this image, when raindrop A disperses light, only red light from the produced spectrum can be seen by the observer because the red light is positioned at a specific angle that allows the light ray to make contact with the observer's eye. Therefore, the sunlight will hit all the raindrops in the surrounding areas in the same way. That is why we see a band of red on the rainbow. Similarly, raindrop B is positioned at a much lower angle in the sky, therefore, red light will not travel to the observer's eye. Rather, the violet light from the produced spectrum is at an appropriate angle to travel to the observer's eye, enabling him/her to see only violet. Therefore, instead of seeing different colors randomly scattered across the sky, we see different bands of colors on the arc.


Additional ResourcesEdit

Refraction and Disperstion Media

Total Internal Reflection

What Causes a Rainbow?

SourcesEdit

"Dispersion" Let's Review: Physics The Physical Setting. Hauppauge, NY: Barron's Educational Series, Inc. 2004.

"Dispersion" Physics: Principles and Problems. Columbus, OH: Glencoe/McGraw-Hill. 1999.

Harris, Tom. "How Rainbows Work" HowStuffWorks. 10 June 2006. <http://science.howstuffworks.com/rainbow.htm>

"Newton, Sir Isaac" Famous Physicists and Astronomers. 9 June 2006. <http://www.phy.hr/~dpaar/fizicari/xnewton.html>

"What causes a rainbow?" HowStuffWorks. 9 June 2006. <http://science.howstuffworks.com/question41.htm>

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