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Optics

Optical Fibres

Optical fibres are made from a core (cylinder) of glass of a certain refractive index, n1, surrounded by a "cladding" of lower refractive index, n2.

If the light meets the interface between core and cladding at the critical angle, c, then i is the maximum angle of incidence which will allow transmission of light down the fibre.

Speed of light in vacuum = v

The refractive index of light going from medium 2 to medium 1 is given by

    2n1 = v2/v1  
and n1 = v/v1   n2 = v/v2
so,   2n1 = n1/n2  

and, as shown previously, this is equal to 1/sinc, where c is the critical angle of incidence for the two media.

Therefore,  n2 = n1sinc
also, sini = n1sinr

and, from the diagram it is clear that

  sinr = cosc
so, sini = n1cosc
  sin2i = n12cos2c
  sin2i = n12(1 - sin2c) = n12 - n22
   
Therefore

 

 

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© David Hoult 2008