# Total internal reflection

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The larger the angle to the normal, the smaller is the fraction of light transmitted, until the angle when total internal reflection occurs. (The colour of the rays is to help distinguish the rays, and is not meant to indicate any colour dependence.)
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Total internal reflection

Total internal reflection is an optical phenomenon. It occurs when light is refracted (bent) at a medium boundary enough to send it backwards, effectively reflecting the entire ray.

When light crosses materials with different refractive indices, the light beam will be partially refracted at the boundary surface, and partially reflected. However, if the angle of incidence is shallower (closer to the boundary) than the critical angle, the angle of incidence where light is refracted so that it travels along the boundary, then the light will stop crossing the boundary altogether and instead totally reflect back internally. This can only occur where light travels from a denser medium to a less dense medium, that is, from the medium with the higher refractive index. For example, it will occur when passing from glass to air, but not when passing from air to glass.

Total internal reflection can be demonstrated using a semi-circular glass block. A ray box shines a light ray onto the glass. The semi-circular shape ensures that a ray pointing towards the center of the flat face will hit the surface at right angles. This prevents refraction at the air/glass boundary.

At the glass/air boundary what happens will depend on the angle. Where θc is the critical angle:

• If θ < θc, as with the blue ray, the ray will split. Some of the ray will reflect off the boundary, and some will refract as it passes through.
• If θ > θc, as with the grey ray, all of the ray reflects from the boundary. None passes through.

The second situation is total internal reflection.

This physical property makes optical fibres useful, and rainbows and prismatic binoculars possible. It is also what gives diamonds their distinctive sparkle, as diamond has an extremely high refractive index.

An important side effect of total internal reflection is the propagation of an evanescent wave across the boundary surface. This wave may lead to a phenomenon known as frustrated total internal reflection.

## Frustrated Total Internal Reflection

While it is true that the creation of an evanescent wave does not affect the conservation of energy under ordinary conditions, i.e. the evanescent wave transmits zero net energy, if a medium with a higher refractive index is placed less than several wavelengths distance from the boundary of the first medium, the strength of the evanescent wave will be large enough to affect a change in the field of the second material. Electrons driven by the field allow energy to flow across the gap and into the second higher refractive index medium.

A common example in everyday use is a beam splitter. A transparent, low refractive index material is sandwhiched between two prisms of another material. This allows the beam to "tunnel" through from one prism to the next in a process very similar to quantum tunneling while at the same time altering the direction of the incoming ray.

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