Question

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.

Hint:

The critical angle for total internal reflection in an optical fiber is determined by the ratio of the refractive indices of the cladding and core.

Answer 1

Correct Answer: 9.3

The critical angle \( \theta_c \) for total internal reflection is given by: \[ \sin \theta_c = \frac{n_{\text{cladding}}}{n_{\text{core}}} \] where \( n_{\text{cladding}} = 1.48 \) and \( n_{\text{core}} = 1.50 \). Substituting these values: \[ \sin \theta_c = \frac{1.48}{1.50} \approx 0.9867 \] Thus: \[ \theta_c = \sin^{-1}(0.9867) \approx 9.30^\circ \] Thus, the critical angle is \( 9.30^\circ \).