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What causes total internal reflection?

There are many everyday uses of the phenomenon known as total internal reflection, from cats eyes on the road to optical fibres delivering the Internet. But what is actually happening when light hits these things?
Brian Taylor from Staffordshire (age 35-44)

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3 Responses

  1. When a light ray crosses the boundary between two materials with different refractive indices, the ray will be partially reflected and refracted (transmitted at a different angle). The refractive indices indicate the difference between the speed of light in the two materials (while matter cannot be faster than light, the speed of light depends on the material). According to Fermat’s principle of least time, the light ray will always take the fastest path. As the speed of light is not the same in the two media, the fastest path between points in the two media is not a straight line, but changes direction at the boundary. So the angle between the ray and the boundary on the side where light is slower (call this inside) will be larger than on the side where light is faster (call this outside).

    As Feynman described it: outside is the beach and inside is the sea, and the fastest path for a rescuer on the beach to get to a drowning person in the sea is the path the refracted light would take. From all angles hitting the waterfront from the beach, you’d only use a limited range of angles in the water to reach the drowning person.

    So you do not have to vary the angles from 0 to 90 degree between the ray and the boundary from inside to get all 0 to 90 degree angles of the refracted rays outside. E.g. for glass approximately 42 to 90 degrees from inside reach all directions outside. At small angles between ray and surface the light is not refracted anymore, but completely reflected (called total internal reflection). There is a “critical angle”, at which the ray from inside is refracted at 90 degrees. (I wish I could attach an image).

    E.g. optical fibres actually only propagate the rays totally that hit the boundary at certain angles (given by the acceptance angle or the numerical aperture of the fibre – at least for multi-modal fibres).

    Thinking of light as a wave, the refracted (and reflected) path of the ray is essentially a result of interference: take all possible paths of waves from the source to a point and combine them there (like water waves). The result will be the reflected and refracted ray. Keep in mind that the wave-length, but not the frequency changes when light moves from one material into the other (i.e. it changes its speed) to get the interference right (see Huygens-Fresnel principle). This then leads to quantum electrodynamics which combines Schroedinger’s equation with Maxwell’s equations, which is beyond the space that I have here ;).

  2. Thanks for such a comprehensive reply. I am still curious to know what is happening at a photon (particle) or wave (energy) interaction between the light and boundary to cause the phenomenon. Are there any other waves that undergo total internal reflection?

  3. HI Brian :).
    The energy possessed by a photon is, initially, absorbed into the molecules of the material of the reflector. This excess ‘vibration’ is later emitted from these molecules as their electrons return to their original orbital locations and for an efficient reflector material, like mercury or silver, most of this energy is emitted as visible light. When the supporting structure is purely transparent as with a fine quality, thin layer of glass, the photon energy released from the mirror is not obviously different in frequency and dispersal. Of course any filtering tints or lack of uniformity e.g. ‘stress changes’ in the materials will create reduced transmission and distortion.
    I hope that this will supplement the excellent description given by Frank Langbein which I found very informative.
    Good Luck,
    Rockno3.

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