The optical fiber structure and mechanism of light transmission is shown in the

Question

The optical fiber structure and mechanism of light transmission is shown in the figure. In order for light propagation to occur, total internal reflection should take place at the core/cladding interface. Consider the situation that we wanted to couple the light into the fiber from free space (air) at its end face, i.e., the beam (1) in the figure. What condition does the incident angle (theta_0) have to meet for the light being able to propagate in the optic fiber? sin theta_0 n_2/n_1 sin theta_0 Squareroot n^2 1 - n^2 2 sin theta_0 > Squareroot n^2 2 - n^2 1

Explanation / Answer

in order for total internal reflection to happen
sin(theta-c)/sin(90) = n2/n1
sin(theta-c) > n2/n1
also, from snell's law
sin(theta-c)/sin(thtea-o) = n1/no
sin(theta-c) = sin(theta-o)*n1/no
sin(theta-o)*n1/no>n2/n1
sin(theta-o)>n2*no/n1^2
hence sin(theta-) > n2/n1 and sin(theta-o)>no/n1

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