To calculate the Numerical Aperture (NA) and the Acceptance Angle of the fiber, we can use the following formulas:

1. Numerical Aperture (NA):

$\text{NA} = \sqrt{n_1^2 - n_2^2}$ Where:

• $n_1$ = Core refractive index.
• $n_2$ = Cladding refractive index.

The relation between $n_1$ and $n_2$ is given by the Relative Index Difference (Δ): $\Delta = \frac{n_1^2 - n_2^2}{2n_1^2}$ From this, we can solve for $n_2$: $n_2 = n_1 \sqrt{1 - 2\Delta}$

2. Acceptance Angle (θₐ):

The acceptance angle (in air) is related to the Numerical Aperture: $\sin \theta_a = \text{NA}$ Then, $\theta_a = \arcsin(\text{NA})$

Given:

• Core refractive index $n_1 = 1.4$
• $\Delta = 0.02$

Let's compute the Numerical Aperture and the Acceptance Angle.### Results:

1. Numerical Aperture (NA): 0.28
2. Acceptance Angle (θₐ): 16.26°

Would you like more details or have any further questions?

Here are 5 related questions for further understanding:

1. How does increasing the core index affect the Numerical Aperture?
2. What is the role of the cladding in fiber optics?
3. How does the relative index difference $\Delta$ influence the fiber's performance?
4. Can Numerical Aperture be greater than 1? Why or why not?
5. How does the acceptance angle impact light propagation within the fiber?

Tip: A larger Numerical Aperture allows the fiber to capture light at wider angles, improving light collection efficiency.