April teaches high school science and holds a master's degree in education.
Refraction explains why light bends in water. But, did you know that mathematical laws determine exactly how light waves are bent? In this lesson, we'll explore the mechanics of wave refraction, including Snell's Law and the index of refraction.
Rainbows and Refraction
Have you ever found a rainbow inside your house? I don't mean the big, round rainbows that you see outside after a rainstorm. I mean the little projections that show up on your walls or floors at certain times of the day. In my house, I get rainbows from the peephole in the front door and the crystal decorations hanging in the windows. The best way to make your own rainbow is to pass white light through a prism. But, what is it that causes rainbows? How can a simple piece of clear glass create so many colors at once? To find out, we'll have to learn all about the principle of refraction.
Refraction and Angles
Refraction is the change in the direction of a wave when it passes from one medium to another. A light wave traveling through air travels at a certain speed. A light wave traveling through glass travels at a different speed. When a light wave travels from the medium of air to the medium of water, its speed changes and it actually bends. This bending is called refraction.
Refraction is often confused with reflection. So, let's make sure we understand the difference between the two. Reflection is a change in the direction of a wave when it strikes a surface. Refraction is a change in the direction of a wave when it passes from one medium to another. Reflection involves bouncing off a surface, while refraction involves passing into a second medium.
In both cases, the process begins with an incident ray that strikes the surface - or enters the new medium - at a certain angle. This angle is called the angle of incidence, the angle between the incident ray and the normal line. The normal is just an imaginary line that's perpendicular to the surface. If this was a reflective surface, then we'd see a reflected ray bouncing off the surface with its own angle of reflection.
A diagram showing the angles of incidence and refraction of a light wave hitting water
But, we're talking about refraction here, so let's say that this line is just the boundary between two different media. A light wave passing from the first medium into the second one will continue as a refracted ray. It will make its own angle of refraction, which is the angle between the refracted ray and the normal line. We usually abbreviate the angles with the symbol 'theta.' We'll put 'theta I' for the angle of incidence, and 'theta R' for the angle of refraction. Notice that the refracted ray doesn't continue along the same trajectory as the incident ray, nor does it make a perfect reflection or a 90-degree angle with the ray. The amount of bending that occurs between the two rays depends on the first medium, the second medium, and the properties of the wave itself.
Index of Refraction
Every different medium has different properties, right? For instance, the properties of glass are different from the properties of outer space. Therefore, light waves travel differently in outer space than they do in glass. Any time a light wave travels through a material, it travels a little bit slower than it would in outer space. The difference between the speed of light in a vacuum and the speed of light in a certain medium is called the index of refraction. It's a number that represents how a medium refracts a light wave.
The index of refraction is different for every medium. It's found using the formula, n = c / v, where c is the speed of light in a vacuum, and v is the speed of light in the medium. The ratio of these two speeds always makes a number that is greater than or equal to 1, because light always travels slower through material than in a vacuum.
So, what about when light travels from one medium to another? For example, what if a light wave is traveling through air, and then it hits a body of water and continues traveling through? Both air and water have their own refractive indices. The index of refraction for air is about 1.0003; for water, it's about 1.3. The larger the index, the slower the light travels through that medium. The index for diamond is 2.4. For sapphire, it's 1.8; and for amber, it's 1.6. So, light travels faster in amber than in sapphire, and faster in sapphire than in diamond.
The index of refraction also affects how a light wave bends when it switches from one medium to another. When the light wave moves from the air to the water, it bends toward the normal, because it is slowing down. The angle of refraction is smaller than the angle of incidence. The difference in size of the angles is directly related to the difference in refractive indices. I'll show you what I mean with a little bit of algebra.
This equation shows the inverse relationship between the angles and indices.
Let's make a ratio of the two refractive indices - the two n values for the air and water. We'll call the index for air nA, and the index of refraction for water nW. The ratio will look like this: nW / nA. The slower medium is on top, while the faster medium is on the bottom. It turns out that these indices are also related to the sine of the angles for each ray of light. Just as nW is larger than nA, the sine of the angle of incidence is larger than the sine of the angle of refraction. This expression reads, 'nW over nA equals sine theta I over sine theta R.'
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So, now we can see the relationship between all the angles and the indices of refraction. We call this expression Snell's Law. It shows how the ratio of the n-values is the inverse of the ratio of the angles. To be more precise, the ratio of the angles of incidence and refraction is equal to the inverse ratio of the indices of refraction. Snell's Law is a great formula to remember, because it helps us predict exactly how light will bend when traveling from one medium to another.
Media and Dispersion
Notice that the equation for Snell's Law shows an inverse relationship between the angles and indices. That is, on one side, we have the refracted medium over the incident medium, whereas on the other side, we have the angle of incidence over the angle of refraction. This is really just a mathematical way of saying that light bends toward the normal in slower media, and away from the normal in faster media.
Remember our example of light traveling from air to water? Since water is a slower medium, then the light waves bend downward, toward the normal. The normal, in this case, is a vertical line. What if our light wave is already in a slower medium, and it travels into a faster one? Let's say our light is traveling through glass and switches over to air at the boundary of the glass. The normal here is actually a horizontal line because of the orientation of the boundary. The light wave travels from a slower medium to a faster one. So, in this case, it bends downward, away from the normal. So, you see, light waves always bend away from the normal in a faster medium and toward the normal in a slower medium.
The frequencies of light hitting a prism will have different angles of refraction.
Some types of media are called dispersive media, meaning that they refract every frequency of light in a different way. A prism is one kind of dispersive media, because it takes white light and separates it into all the colors of a rainbow. What's really happening is that each different frequency of colored light in the spectrum is being refracted at a different angle by the prism itself. Instead of having just one angle of refraction for the whole light beam, there are many separate angles for all the separate frequencies. The result of this phenomenon is dispersion: the separation of waves of various frequencies due to their differences in refractive angles. Dispersion is the reason we can see the color spectrum when passing white light through a prism, a crystal, or even a front door peephole. It also plays a role in creating the beautiful rainbows that we see outside.
When a wave passes from one medium to another, it bends, or changes in direction. This phenomenon is known as refraction. An incident ray traveling in one medium makes an angle of incidence with the normal line. The bending of this wave results in the refracted ray, which travels through the second medium at an angle known as the angle of refraction.
If the second medium is slower, then the wave bends toward the normal. If the second medium is faster, then it bends away from the normal. The number that describes how a medium refracts a wave is called the index of refraction. A ratio of the two indices is actually related to the ratio between the angles of incidence and refraction. Snell's Law states that the ratio of the angles of incidence and refraction is equal to the inverse ratio of the indices of refraction.
Refraction of light waves explains the dispersion of white light when it passes through a prism. Each frequency of light is refracted at a different angle, so that all frequencies are separated to create a visible rainbow.
At the end of this lesson, you'll be able to:
Differentiate between refraction and reflection
Explain what causes refraction
Relate the index of refraction to how a wave bends in relation to the normal
Describe the inverse relationship indicated by Snell's Law
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