In optical fibre, refractive index of inner part is 1.68 and refractive index of outer part is 1.44. The numerical aperture of the fibre is

Options

A. 0.5653
B. 0.6553
C. 0.7653
D. 0.8753

Answer

To find the numerical aperture (NA) of an optical fiber, we can use the formula:

\[ NA = \sqrt{n_1^2 - n_2^2} \]

where:
- \( n_1 \) is the refractive index of the core (inner part),
- \( n_2 \) is the refractive index of the cladding (outer part).

### Step-by-Step Solution:

1. **Identify the Refractive Indices**:
- Given:
- Refractive index of the core, \( n_1 = 1.68 \)
- Refractive index of the cladding, \( n_2 = 1.44 \)

2. **Square the Refractive Indices**:
- Calculate \( n_1^2 \):
\[ n_1^2 = (1.68)^2 = 2.8224 \]
- Calculate \( n_2^2 \):
\[ n_2^2 = (1.44)^2 = 2.0736 \]

3. **Subtract the Squares**:
- Now, subtract \( n_2^2 \) from \( n_1^2 \):
\[ n_1^2 - n_2^2 = 2.8224 - 2.0736 = 0.7488 \]

4. **Take the Square Root**:
- Finally, take the square root of the result:
\[ NA = \sqrt{0.7488} \approx 0.8657 \]

5. **Round the Result**:
- Rounding \( 0.8657 \) gives approximately \( 0.87 \).

6. **Match with Options**:
- The closest option available is \( 0.8753 \), which can be considered as the final answer.

### Final Answer:
The numerical aperture of the fiber is approximately \( 0.8753 \).