Is the color of light determined by its frequency or its wavelength?

Email Received:

I am a student at ***** competing in the Science Olympiad and would be extremely grateful to you if you could answer a question regarding physical optics. Is the color of light determined by its frequency or its wavelength? Also, if a ray of colored light, say red, were to pass from air into glass, theoretically, would the color change while inside the glass? I would greatly appreciate it if you could answer these questions because none of the teachers in my school seem to be able to.

Tedís Response:

Most people probably would say that a light's color is always dependent on its wavelength. But this is true only if the light is traveling through only one medium, such as air. Indeed, in a single medium, different wavelengths of light appear as different colors; and the longer the wavelength, the lower the frequency of the light.

If the light enters another medium, such as glass, then the wavelength will change. However, the color will remain the same because the frequency of that color of light remains the same from one medium to another. The color always is dependent upon the light's frequency, which is the number of waves of the light that pass a given plane in space per second (that is, the number of cycles per second). If the color of the light always was dependent upon its wavelength, then its color would change when it enters a medium with a different index of refraction; but it does not.

For instance, if you observe a beach ball sitting near the edge of a swimming pool, then jump into the swimming pool and look up at the beach ball while your head is submerged under water, all the colors on the beach ball will appear the same as they did when you were standing in the air. What changes when light goes from one medium to another are both the speed of the light and the wavelength of the light. But the frequency of the series of light waves does not change; therefore, the color does not change.

Let's say that red laser light is aimed at a slab of dense crown glass with an index of refraction of 1.60. The light enters one side, passes through the glass, and emerges from the other side. The beam of light will be the same shade of red both outside and inside of the glass. The reason for this is because of the following important formula:

As the light enters the glass, it slows down. At the same time, the wavelength of the light also shortens proportionally. So the frequency (and, therefore, the color) remains the same, because the same number of waves are passing a fixed plane in space per second (cycles per second), whether the light is inside the glass or in the air outside. Here is a graphic representation of this:

          Snellís Law:

As you can see, the wavelength of the red light shortens in the glass, and so does the speed of the light. But the frequency remains the same, and so does the color. Thus, red light of wavelength 700 nm in air will appear the same color as red light of wavelength 438 nm in this type of glass. (Note that light with a wavelength of 438 nm in air would appear indigo, somewhere between blue and violet, in color; but this same wavelength in dense crown glass would be red.)

The same circumstances would be true if this were a huge container of water with glass on all four sides.  If you were submerged in the water, and the red laser light were shining into one side, then passing through the glass and the water and into your eyes, it would appear as red to you as if you were outside of the container and looking at the same laser light in the air. The index of refraction of water is about 1.33, so the wavelength of the red light passing through the water would be 700 nm ų 1.33 = 526 nm.

A simple way to test to see if the red color of an object appears the same in different media is to fill a glass with water and get a red straw. Notice how red the straw looks in the air. Place the straw on the other side of the glass of water and view it through the water and the glass; the color will not change. Then immerse the straw in the water and look at it from above, directly into the water, and then through the side of the glass. The redness of the straw will be the same, no matter how you view it, even though the wavelength of the red light is changing as it goes from one medium to another.

Now, let's say you and a friend are going swimming. Before you jump into the pool of water, you can see that he is wearing red swim trunks. If you jump in first, submerge yourself in the water, and look up at your friend still standing at the edge of the pool, the red color of his trunks will appear the same as they did before you jumped into the pool. Next, he will jump into the pool. If you stand with your head above the water, you can look at his trunks that are below the surface of the water, and they will be the same red color. Finally, if you immerse yourself entirely in the water, you will perceive no variation in the red color of the trunks.

In two of the cases, when the red light is passing from air into water or water into the air, the wavelength changes, but the frequency of the red light remains the same. So the color will remain constant, even though the wavelength changes when moving from one medium to another, since it is the frequency of the light that determines its color in all media.

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