Course:Total internal reflection

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Total Internal Reflection, or TIR as it is often abbreviated, is a very unique optical phenomenom.

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:

  • Partially refract out and partially reflect back inside (almost the same as the previous example)
  • Completely reflect back (with no refraction out)

When the latter occurs, we talk about Total internal reflection.


Inside the refractometer: Total Internal Reflection

When light travels from an optically denser material (with higher index of refraction) to an optically rarer material (with lower index of refraction), all light that reaches the boundary of the two materials will be either reflected inside the denser material or refracted into the rarer material, depending on the angle of incidence of the light.

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). 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.

N.B.: In this example, the light seems to come from 3 light sources, but the principle is the same when coming from a single point.

In a hemicylinder, the incident and exiting ray always reach the boundary at a 90 degree angle when directed to the center. Refraction doesn't occur when a light ray is at 90 degrees to the boundary. A hemicylinder is used so there will be no refraction of the light entering nor leaving the denser material.

The standard gemological refractometer can make use of this phenomenon because the reflected rays of light will appear as a light area on the scale, while the refracted rays are not visible (and therefore appear black). The light/dark boundary shown on the scale of the refractometer is a visible representation of the critical angle.

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


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