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. 0.6653
C. 0.7653
D. `08653`

Answer

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

\[ \text{Numerical Aperture (NA)} = \sqrt{\mu_1^2 - \mu_2^2} \]

where:
- \(\mu_1\) is the refractive index of the inner part of the fiber (core),
- \(\mu_2\) is the refractive index of the outer part of the fiber (cladding).

### Step 1: Identify the refractive indices
Given:
- \(\mu_1 = 1.68\)
- \(\mu_2 = 1.44\)

### Step 2: Square the refractive indices
Calculate \(\mu_1^2\) and \(\mu_2^2\):
\[ \mu_1^2 = (1.68)^2 = 2.8224 \]
\[ \mu_2^2 = (1.44)^2 = 2.0736 \]

### Step 3: Subtract the squares
Now, subtract \(\mu_2^2\) from \(\mu_1^2\):
\[ \mu_1^2 - \mu_2^2 = 2.8224 - 2.0736 = 0.7488 \]

### Step 4: Take the square root
Now, take the square root of the result to find the numerical aperture:
\[ \text{NA} = \sqrt{0.7488} \approx 0.8653 \]

### Final Answer
Thus, the numerical aperture of the optical fiber is approximately \(0.8653\).

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