The light could be guided by i) refraction (using lenses), ii)reflection and iii) total internal reflection. Guidance by refraction and reflection is lossy and hence is limited only to shorter distances. Guidance by total internal reflection is most often used as the losses are only due to absorption in the medium.
A common example is the propagation of light in an optical fiber which in its simplest form consists of a circular core of uniform refractive index surrounded by a cladding of slightly lower refractive index. The light is launched into the entrance face of the fiber. The light is propagated by the total internal reflection at the interface between core and cladding. However the rays incident at angles larger than a certain angle, called the cut-off angle, suffer both refraction and reflection at the interface between the core and the cladding. They, therefore, are not guided. Due to this the optical fiber has a numerical aperture. The numerical aperture is given by the square root of (n12-n22). Typical values of numerical aperture lie between 0.1 and 0.3.
Consider the figure which is a section of the optical fiber. The refractive indices of the core and the cladding are n1 and n2 respectively. The fiber is normally in air (n0=1) but could also be in a medium of refractive index n0.The axis of the cylindrical structure is the optical axis. A ray is incident at an angle i at the entrance face and refracted into the core. It then strikes the core-cladding interface at a certain angle. If this angle exceeds the critical angle, it is totally reflected and strikes the interface on the other side of the axis. Here it is again totally reflected. This process is repeated till the ray emerges out of the fiber at the other end. The ray is thus guided by total internal reflection.
The angle of incidence at the entrance face for which the ray strikes the core-cladding interface at the critical angle is called the cut-off angle. The ray is guided for all the angles of incidence smaller than the cut-off angle at the entrance face. Also the numerical aperture is equal to n0 times the sine of cut-off angle. However, if the angle of incidence at the interface is less than the critical angle, both reflection and refraction takes place. Due to refraction at each incidence on the interface, the light beam dies off over a certain distance. There is no guidance.
The light path under varying conditions of input parameters can be studied by the following:
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