GATE EC 2021 Set 1 — Question 35
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Electromagnetics → Waveguides & Optical Fibers → Light Propagation in Fibers
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Question
The refractive indices of the core and cladding of an optical fiber are and , respectively. The critical propagation angle, which is defined as the maximum angle that the light beam makes with the axis of the optical fiber to achieve the total internal reflection, (rounded off to two decimal places) is ________ degree.
Correct answer
9.3 to 9.44
Solution
Given:
Refractive index of core,
Refractive index of cladding, Let be the critical angle at the core-cladding interface. By Snell's law:The propagation angle is the angle the light beam makes with the fiber axis. The angle of incidence at the core-cladding interface is .
For total internal reflection (TIR) to occur, the angle of incidence must be greater than or equal to the critical angle:The maximum propagation angle (critical propagation angle) is:Alternatively, using the relation :Rounding off to two decimal places, the value is .
Refractive index of core,
Refractive index of cladding, Let be the critical angle at the core-cladding interface. By Snell's law:The propagation angle is the angle the light beam makes with the fiber axis. The angle of incidence at the core-cladding interface is .
For total internal reflection (TIR) to occur, the angle of incidence must be greater than or equal to the critical angle:The maximum propagation angle (critical propagation angle) is:Alternatively, using the relation :Rounding off to two decimal places, the value is .
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