Course:Refraction

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Main article: refraction
Refraction of a light ray

Refraction means the bending of light inside a material, such as a gemstone.
When light travels from air into an optically denser material (such as a gemstone), the light will appear to slow down inside that gemstone and it will change direction. The amount at which this light apparantly slows down and changes direction is dependent on the index of refraction of the gemstone.
Note that we say "the light will appear to slow down". That is because in reality it doesn't slow down atall, but it looks like it does. Although that is an advanced topic, it's best not to learn bad habits.

Every gemstone has its own index of refraction which makes refraction a very good aid in identifying the stone. However some stones have similar indices of refraction that overlap. When an index of refraction is given for a stone in a textbook (or here), it does not mean that the gemstone will have that ideal value. Impurities inside the gem may cause it to deviate slightly. That is why usually a range of possibilities is given.

For instance the gemstone spinel can have an index of refraction ranging from 1.712 to 1.736 and that can be confusing at first.

In the image on the right you will see the bending of light when it enters a gemstone (light coming from air). As you can see, the refracted ray makes a smaller angle (r) to the normal than the incident ray (i) and we will discuss that a bit more.
In a later chapter you will learn that not all the light from the incident ray is refracted inside the stone, some will be reflected. But we are concentrating on the refracted part only for now.


Below is a small animation of how light behaves when it travels from air in an optically denser medium and then in air again. Play the video a few times and observe what is happening.
The red arrow represents the light and you will notice that when it reaches the square piece of glass, we draw in the normal (the blue line). Then it travels inside the glass, but it bends and travels slower.
The light will then reach the lower boundary between the glass and air again. You see that it bends again and, apparantly, picks up speed.

The image on the right of the animation shows the path the light takes represented by the black line. It seems that the light before it entered the glass and the light that left the glass are traveling in the same direction, they are parallel. And indeed they are parallel.
In the next image the angles are drawn in and you will see that both these angles are exactly the same. We always measure angles in reference to the normal (the blue perpendicular lines).

click to enlarge
click to enlarge

When the light travels from air into the glass, it is refracted (bent) towards the normal. When it travels from glass into air, it is refracted away from the normal.

As always there is an exception to the rule and that exception is that if the light reaches a boundary at an angle of 90° (so parallel to the normal), the light will not be refracted. It will still appear to travel slower, but it will not bend.
This exception can be very convenient and we indeed make good use of it when we construct a refractometer.

In this animation light is traveling from air into a glass hemicylinder. One can imagine the hemicylinder to be half a cylinder with the centerpoint located at the red dot.
Every light ray that travels to the center of a cylinder (the red dot) will reach the boundary of that cylinder at exactly 90°. Therefor the light will not refract.

When we cut the cylinder in half to create a hemicylinder (as shown in the animation), it still works aslong as the light comes from the domed side. Such a hemicylinder is used in the standard gemological refractometer.

If we needed to draw in a normal, it would be at the exact position and direction as the red arrow.


You will often read about the index of refraction instead of refractive index and think they are the same, but they aren't the same thing.
This has to do with the fact that when we think of light, usually we think of it as the white light coming from the sun (or a lightbulb). As you will learn later in the dispersion chapter, that white light is made up of many colors and all these colors refract differently inside an optically denser medium.
As you can imagine it is not very useful to have to calculate the amount of bending all of these different colored lightrays undergo. Instead we want to measure it for just one color.
When we speak of the index of refraction, we mean the whole range of bending of white light. From red to blue light.
When we use the term refractive index, we refer to the amount of bending for just one color.

Ofcourse we need to pick a color for this refractive index and in gemology we use yellow light with a wavelength of 589.3 nm, which is sodium light. Every reference in gemological textbooks uses this lightsource unless otherwise stated.

In optics, and optics related topics like gemology, the index of refraction is abbreviated with the small letter n and the yellow sodium light is abbreviated with the capital letter D (usually in subscript). So if you read something like nD = 1.714, you know that it is the refractive index measured with sodium light.

In many formulas you will see things as n1 and n2 and it is important that you understand what they mean.

  • n1 means "the index of refraction of the material where the light is coming from"
  • n2 means "the index of refraction of the material where the light is traveling to"

If light will be traveling from air to a gemstone, then the air is n1 and the gemstone is n2. But if the light is traveling from the gemstone to air, the gemstone will be n1 and the air will be n2.

Extra

For those who like math, we can calculate the index of refraction is a few ways, depending on which constants we work with.
One way is through the amount of slowing down of the light. The other is by measuring the angles of the incident ray and the refracted ray.

When we consider the speed of light, we could write:

<math>n = \frac{velocity\ of\ light\ in\ air}{velocity\ of\ light\ in\ medium}</math>


The speed of light in air is about 300,000 km/second. If the speed of light inside the gemstone is 150,000 km/sec, then we could write:

<math>n = \frac{300,000}{150,000}\ =\ 2</math>


If you go back to the very first image on this page, you will see the angles of the incident ray and the refracted ray indicated as i and r.
We could use these angles to determine the refractive index.

<math>Index\ of\ refraction = \frac{\sin(angle\ of\ incidence)}{\sin(angle\ of\ refraction)}\ =\ \frac{\sin i}{\sin r}</math>


When the angle of incidence (i) is 60° and the angle of refraction (r) is 30°, that would be:

<math>Index\ of\ refraction = \frac{\sin 60}{\sin 30}\ =\ 1.732</math>


The latter is what is called "Snell's Law" which also states that the incident ray, the normal and the refracted ray all lay in the same plane. In this case the plane of your computer monitor.

Notice that we used n and index of refraction interchangable. That is because we are just doing theory here and they are the same. If we wanted to do that for sodium light (nD) we would need to specify that.