The glass of optical fibre has a refractive index 1.55 and cladding with another glass of refractive index 1.51. When the surrounding medium is air, the numerical aperture will be

Options

A. 0.625
B. `0.350`
C. `0.528`
D. 0.704

Answer

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

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

where:
- \( n_1 \) is the refractive index of the core (glass of optical fiber),
- \( n_2 \) is the refractive index of the cladding.

### Step-by-step Solution:

1. **Identify the Refractive Indices**:
- The refractive index of the core, \( n_1 = 1.55 \).
- The refractive index of the cladding, \( n_2 = 1.51 \).

2. **Substitute the Values into the Formula**:
\[ \text{NA} = \sqrt{(1.55)^2 - (1.51)^2} \]

3. **Calculate \( n_1^2 \) and \( n_2^2 \)**:
- Calculate \( (1.55)^2 \):
\[ (1.55)^2 = 2.4025 \]
- Calculate \( (1.51)^2 \):
\[ (1.51)^2 = 2.2801 \]

4. **Subtract \( n_2^2 \) from \( n_1^2 \)**:
\[ 2.4025 - 2.2801 = 0.1224 \]

5. **Take the Square Root**:
\[ \text{NA} = \sqrt{0.1224} \approx 0.349 \]

6. **Round the Result**:
- The numerical aperture can be approximated to \( 0.350 \).

### Final Answer:
The numerical aperture (NA) of the optical fiber is approximately \( 0.350 \).