Find NA and acceptance angle of a fiber with core index 1.4 and Δ = 0.02.

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.

Learn how to calculate the Numerical Aperture (NA) and Acceptance Angle for an optical fiber with a core refractive index of 1.4 and a relative index difference (Δ) of 0.02. This tutorial includes step-by-step calculations using optical fiber theory and formulas. Ideal for physics or optics students at the undergraduate level.

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