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 will use the formula:

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

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

### Step 1: Identify the refractive indices
From the problem, we have:
- \( n_1 = 1.55 \) (refractive index of the optical fiber),
- \( n_2 = 1.51 \) (refractive index of the cladding).

### Step 2: Square the refractive indices
Now, we will square both refractive indices:
- \( n_1^2 = (1.55)^2 = 2.4025 \)
- \( n_2^2 = (1.51)^2 = 2.2801 \)

### Step 3: Subtract the squares
Next, we will subtract \( n_2^2 \) from \( n_1^2 \):
\[ n_1^2 - n_2^2 = 2.4025 - 2.2801 = 0.1224 \]

### Step 4: Take the square root
Now, we will take the square root of the result from Step 3 to find the numerical aperture:
\[ NA = \sqrt{0.1224} \approx 0.350 \]

### Final Answer
Thus, the numerical aperture of the optical fiber is approximately:
\[ NA \approx 0.350 \]

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