Course:Total internal reflection

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The following topics should be fully understood before studying this article.

Main article: brilliance

Total Internal Reflection, or TIR as it is often abbreviated, is a very unique optical phenomenom. Although many aspiring gemologist struggles with this topic, it is fairly easy to understand aslong as you keep a few basic rules in mind.

When light travels through air and reaches an object with a different refractive index (like for instance water, with a RI of about 1.3), the light will be refract (or bend) inside that object (the water). Although that is true, it is not the whole truth.
While some light refracts inside the water, other parts will reflect off the water.

In the previous example, the light is traveling from air with an RI of 1, to water with an RI of 1.3.
We could also say that light is traveling from an optically rarer medium (the air) to an optically denser medium (the water).

Optically rarer means that the medium (material) has a lower refractive index compared to another medium, the material with the higher RI is called the optically denser medium

Although the previous doesn't have anything to do with TIR, it is important to know that light traveling from an optically rarer medium to an optically denser medium will always both refract and reflect.

When we let the light travel from the optically denser material (the water) to an optically rarer medium (the air), that always rule is not valid anymore. Light traveling from the denser to the rarer medium will either:

  • Completely reflect back (with no refraction out)
  • Partially refract out and partially reflect back inside (almost the same as the previous example)
  • Continue to travel along the boundary of two media

When the first happens, we talk about Internal reflection and this depends on the angle at which the ray of light hits the boundary between the optically denser and the optically rarer medium.
That specific angle, where it will either refract (plus some reflection) or totally reflect (with no refraction), is termed the critical angle.

Total Internal Reflection can only happen when light is traveling from an optically denser to an optically rarer medium

This theory is very important to understand as it the basic principle behind gemcutting and the refractometer.
In diamond the angles at which the pavillion facets are cut are determined by the critical angle (abbreviated by ca).
The refractometer makes use of this phenomenom by showing which parts of the light on the refractometer's scale are from reflection and which from refraction.

The three behaviors a ray of light can exhibit when traveling inside an optically denser medium (like glass) towards an optically rarer medium (as in air)

In the image above the 3 possibilities of light traveling from air into an optically denser material and then towards an optical rarer material (air again) are illustrated. We assume that the hemicylinder (half a cylinder) is glass (RI = 1.54) and the surrounding medium is air (RI = 1).
The dashed line marked "N" and "O" is an imaginary line cutting through the middle of a hemicylinder, this imaginary line is termed the "normal" and this line is the base of the angles. This line is perpendicular to the flat top of the hemicylinder. A hemicylinder was chosen for illustration as any line going to the center point of a cylinder will reach the outer boundary at 90° as illustrated by the dotted lines. Any ray of light reaching a boundary at 90° will not be refracted.
The critical angle (ca) is the outer limit of the area between the normal and the red line. You can think of it as a turning point.

The blue ray (left) travels inside the hemicylinder at an angle larger than the critical angle and the light will be internally reflected. The green ray (middle) travels at an angle smaller than the critical angle and will refract out, with some reflection (the dashed-dotted line). The red ray travels at exactly the critical angle and will continue its path along the boundary of the hemicylinder and the surrounding air.

Note: the colored lines are differently colored for illustration purposes, they could all have been blue, or green or red (or any other color).

Total internal reflection in facetting

Total Internal Reflection in a Diamond.
Light reaching the facet at an angle larger than the critical angle will be reflected.

Schematic overview of the Total Internal Reflection in different cuts

Total internal reflection in a refractometer

The refractometer is one of the most important tools in determative gemology and although you don't need to know how it works in order to operate it, the knowledge will make you much smarter and it is quite satisfactory to the mind if you do understand it.

While we talked about light traveling from a gemstone (such as diamond) to an optically rarer medium (the air), the theory works for every two materials with different refractive indices that are in contact with eachother. The rule that the light should travel from the material with the higher refractive index (the denser medium) to a material with a lower refractive index (the rarer medium) still applies. It doesn't work vice versa.

For every two media in contact in which light is traveling from the denser to the rarer medium, the dividing line where either the ray of light is totally reflected or refracted is fixed and can be calculated. This dividing line is named the critical angle (ca)
Inside the refractometer: Total Internal Reflection

On the left you find an image showing the critical angle as the red line.
When light reaches the boundary of the two materials at an angle larger than this critical angle (the blue line), the ray of light will be totally reflected back into the denser material. Light reaching the boundary at an angle smaller than the critical angle will be refracted out of the denser medium (and a small amount will be reflected) into the rarer medium (the green line). All light traveling precisely on the critical angle will follow the path of the boundary between the two materials.


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