GATE 2021 EC – Question 35
The refractive indices of the core and cladding of an optical fiber are 1.50 and 1.48, 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.
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Correct answer: 9.32 to 9.42
Explanation
Total internal reflection at the core-cladding boundary needs the ray to meet the boundary at an angle of at least $\theta_c=\sin^{-1}\frac{n_2}{n_1}$ from the normal, so the ray makes at most $90^\circ-\theta_c$ with the axis: $\cos\theta=\frac{n_2}{n_1}=\frac{1.48}{1.50}$, giving $\theta=\cos^{-1}(0.98667)\approx9.37^\circ$.