In an optical fibre ,the refractive indices of the core and the cladding are given by `n_(1)` and `n_(2)` respectively . Light can travel through the optical fibre if

Options

A. `n_(1) = n_(2)`
B. `n_(1) lt n_(2)`
C. `n_(1) gt n_(2)`
D. `n_(1) = (n_(2))/(3)`

Answer

To determine the condition under which light can travel through an optical fiber, we need to analyze the refractive indices of the core and cladding of the fiber. The refractive indices are denoted as \( n_1 \) for the core and \( n_2 \) for the cladding.

### Step-by-Step Solution:

1. **Understanding Optical Fiber Structure**:
- An optical fiber consists of a core, cladding, and a protective jacket. The core is the central part where light travels, and the cladding surrounds the core.

2. **Refractive Indices**:
- The refractive index of the core is \( n_1 \) and that of the cladding is \( n_2 \). For light to travel through the optical fiber, it must undergo total internal reflection.

3. **Condition for Total Internal Reflection (TIR)**:
- Total internal reflection occurs when light attempts to move from a denser medium (higher refractive index) to a rarer medium (lower refractive index). This means that for light to be confined within the core of the optical fiber, the core must have a higher refractive index than the cladding.

4. **Inequality Relation**:
- The condition for TIR can be expressed mathematically as:
\[ n_1 > n_2 \]
- This inequality indicates that the refractive index of the core (\( n_1 \)) must be greater than that of the cladding (\( n_2 \)) for light to travel through the fiber.

5. **Conclusion**:
- Therefore, the light can travel through the optical fiber if the refractive index of the core is greater than that of the cladding, which is represented by the relation:
\[ n_1 > n_2 \]