If `mu` and `mu_(2)` are the refractive indices of the materials of core and cladding of an optical fibre, then loss of light due to its leakage can be minimised by having

Options

A. `mu_(1)gtmu_(2)`
B. `mu_(1)ltmu_(2)`
C. `mu_(1)=mu_(2)`
D. none of these

Answer

To solve the problem regarding minimizing light loss due to leakage in an optical fiber, we need to understand the relationship between the refractive indices of the core and cladding materials.

### Step-by-Step Solution:

1. **Understanding Optical Fiber Structure**:
- An optical fiber consists of two main parts: the core and the cladding. The core is the central part through which light travels, while the cladding surrounds the core and has a lower refractive index.

2. **Refractive Indices**:
- Let \( \mu_1 \) be the refractive index of the core material.
- Let \( \mu_2 \) be the refractive index of the cladding material.
- For effective light transmission, the refractive index of the core must be greater than that of the cladding, i.e., \( \mu_1 > \mu_2 \).

3. **Total Internal Reflection**:
- The principle that allows light to be guided through the core of the fiber is called total internal reflection. This phenomenon occurs when light travels from a medium of higher refractive index (core) to a medium of lower refractive index (cladding).
- For total internal reflection to occur, the condition \( \mu_1 > \mu_2 \) must be satisfied.

4. **Minimizing Light Loss**:
- To minimize the loss of light due to leakage, it is essential to ensure that total internal reflection is maintained. This can be achieved by ensuring that the refractive index of the core is greater than that of the cladding.
- Therefore, the condition \( \mu_1 > \mu_2 \) is necessary to minimize light loss.

5. **Conclusion**:
- The correct condition to minimize light loss due to leakage in an optical fiber is that the refractive index of the core must be greater than that of the cladding, i.e., \( \mu_1 > \mu_2 \).

### Final Answer:
To minimize the loss of light due to its leakage in an optical fiber, it is necessary to have \( \mu_1 > \mu_2 \).

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