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Chapter 20: Problem 2701

If \(\mathrm{M}_{1} \& \mathrm{M}_{2}\) are the refractive indices of the material of core and cladding of an optical fiber, than the loss of light due to its leakage can be minimized by having (A) \(\mathrm{M}_{1}>\mathrm{M}_{2}\) (B) \(\mathrm{M}_{1}<\mathrm{M}_{2}\) (C) \(\mathrm{M}_{1}=\mathrm{M}_{2}\) (D) None of these

Short Answer

Expert verified
The loss of light due to leakage in an optical fiber can be minimized by having the refractive index of the core (M1) greater than the refractive index of the cladding (M2). This condition ensures total internal reflection within the core and minimizes light leakage. Therefore, the correct answer is: (A) M1 > M2

Step by step solution

01

Recall the condition for total internal reflection (TIR)

Total internal reflection occurs when a light wave travels from a medium with a higher refractive index (M1) to a medium with a lower refractive index (M2) and the angle of incidence is greater than the critical angle. The critical angle is given by the formula: \[ \theta_c = \sin^{-1} \left(\frac{M2}{M1}\right) \] Where θc is the critical angle, M1 is the refractive index of the core, and M2 is the refractive index of the cladding.
02

Determine the condition for minimizing light leakage

To minimize the loss of light due to leakage, the total internal reflection must be ensured inside the optical fiber. Based on the TIR condition, this can be achieved when: 1. The refractive index of the core (M1) is greater than the refractive index of the cladding (M2). 2. The angle of incidence is greater than the critical angle. From the choices given, the correct answer is: (A) M1 > M2 This condition ensures that the light will undergo total internal reflection within the core and minimize the loss of light due to leakage into the cladding.

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