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# The Science of Rainbows

Emmette Cox
Product Management Coordinator for Physical Science

Studying rainbows can provide much understanding about the behavior of light, and about waves in general. When the different colors of light separate through a process called dispersion, it creates the spectrum of a rainbow. This happens because the different colors of light are actually different wavelengths of light, each of which refracts, or bends, at a different angle when passing from the medium of air to the medium of water. Light refracts when it changes media because light travels at different speeds in different media. What we see as light is just one part of a larger spectrum called electromagnetic radiation, which includes RADAR, radio waves, x-rays, and gamma rays.

### Background

#### Historical discoveries

People have studied the nature of light since ancient Greece. It was known for years that a piece of glass, such as a prism, could create a rainbow, but no one was sure how. It was once thought that the prism colored the light from the sun as that light passed through the glass.

The first real answers to the mysteries of rainbows came around 1666 from English physicist Isaac Newton. Many people have heard of Newton. There is the familiar story of the apple falling on his head and his theory of gravity. You may have heard of his laws of motion, or even that he was a great mathematician who developed the branch of math known as calculus. Newton also did a great deal of work in the field of optics, which is the study of the nature of light and its interaction with matter.

Newton discovered that when light passed through a prism, the different colors of light were bent or refracted by a different amount. Light entering the prism separated into different colors rather than being colored by the prism. Like other scientists studying light, Newton allowed light to pass through a prism and create a rainbow, or spectrum as Newton called it. Newton, however, did something no one else had done before—he let the colored light pass through a second prism. The second prism recombined the colored light into white light. Today, students learn pretty early in school that white light is composed of different colors of light, but in 1666 this was a new idea.

#### Rainbows

Raindrops are obviously different from glass prisms, but those water droplets can bend or refract light the same way. Raindrops suspended in air take on the shape of a sphere. As light passes from the air to the water, the light rays bend, just as when light passes from air through the glass of a prism. The accompanying diagram (Fig. 1) illustrates this.

Figure 1

In the diagram, the circle represents a raindrop. As white light from the sun hits the drop, the light refracts. The blue light bends more than the red. The other colors between blue and red bend by different amounts, and the colors spread out to form the spectrum. Our diagram shows only the red and violet colors to simplify the illustration. Light also is reflected at the back side of the raindrop. Some of the light makes it through the raindrop, but the part that reflects off the back side of the raindrop is refracted again as it leaves the water and re-enters the air.

As with a prism, light hitting the raindrop spreads out as the different colors refract or bend by different amounts, and we get a spectrum. Thanks to Newton, we know that white light is made up of different colors.

What causes light to refract? Light bends or refracts when it passes from one medium to another, such as when a light ray passes from air to water or water to air. Light travels more slowly in media that are denser, and when light passes from one medium to another at an angle this causes the ray to bend. Imagine a shopping cart rolling from pavement to grass. If the cart travels from the pavement onto the grass so both front cart wheels reach the grass at the same time, the cart slows down. If the cart passes from pavement to grass at an angle, with wheels on one side reaching the grass and slowing down before wheels on the other side, then the cart turns. This is similar to how light bends when it passes from air to water.

And what makes the colors of light different from each other? What we see as light is actually a small part of a larger spectrum called the electromagnetic spectrum, which includes radio waves, microwaves, infrared light, visible light, ultraviolet light, x-rays, and gamma rays. Each type of wave and each color have a different wavelength. Colors near the blue end of the spectrum have a shorter wavelength; colors near the red end have a longer wavelength (Fig. 2).

Figure 2  The blue wave has a shorter wavelength than the red wave.

Wavelengths in the electromagnetic spectrum range from 100 million meters (extremely low frequency [ELF] radio waves) to 1 trillionth of a meter (gamma waves). The part of the spectrum that we can see, visible light, ranges from 360 nm at the blue end of the spectrum to 760 nm at the red end. The symbol “nm” means nanometers. A nanometer is 1 billionth of a meter. The small marks on a meter stick represent millimeters. Between the ends of the meter stick are 1,000 of those marks. To measure nanometers would require 1,000,000,000 marks between the ends.

To see a rainbow, rain droplets must be in the air, such as after a brief shower, and the sun needs to be behind you at a low angle. This happens more often in some places than in others. Did you know rainbows happen every day in Hawaii? In fact, Hawaii is known as the Rainbow State.

Raindrops separate or disperse the visible, white light from the sun into the familiar rainbow we all know: red, orange, yellow, green, blue, indigo, and violet. You may be familiar with the acronym Roy G. Biv, a helpful mnemonic for remembering the colors of the rainbow. But what makes a rainbow appear in the sky at certain times and not others?

A rainbow forms when water droplets are suspended in the air such that the light is refracted from 40 to 42° from the original direction. The rainbow is not actually located where it appears to be but is an image that depends on the viewer’s location. The rainbow actually should make a complete circle but the bottom half is blocked from view by the ground. Lucky passengers in an airplane may see a rainbow that is a complete circle.

### Resources

We recommend the following products to help you teach about light waves and their properties.