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Total internal reflection:
When the incident angle $Φ_1$ is higher than critical incident angle $Φ_c$ the whole path of the light is reflected back in the first medium. This is known as Total Internal Reflection (TIR).
$$Φ_1\gtΦ_c …………. Condition \ \ \ for \ \ \ TIR$$
Acceptance angle:
Maximum angle to the axis of the core that light may enter the fiber in order to be propagated in the form of total internal reflection within the fiber core is called as Acceptance angle α.
The acceptance cone decides the propagation of signal which is defined by conical half angle α.
Critical angle:
At a specific value of incidence angle the angle of refraction is 90°. This incidence angle is known as critical angle $θ_c$.
It is the angle above which total internal reflection takes place. Refer figure 2.
$$θ_{c }=sin^{-1 } \left(\frac{n_2}{n_1} \right)$$