Here is a Python program that calculates the numerical aperture (NA) of a fiber optic cable based on the refractive indices of the core and cladding and visualizes light acceptance.

pythonCopy code
import numpy as np
import matplotlib.pyplot as plt

# Define refractive indices
n_core = 1.48  # Refractive index of the core
n_cladding = 1.46  # Refractive index of the cladding

# Calculate Numerical Aperture (NA)
NA = np.sqrt(n_core**2 - n_cladding**2)
print(f"Numerical Aperture (NA): {NA:.4f}")

# Plot light acceptance
theta = np.linspace(0, 90, 500)  # Angles in degrees
theta_rad = np.radians(theta)  # Convert to radians
acceptance = np.sin(theta_rad)  # Sin of angles

# Define the maximum acceptance angle based on NA
max_acceptance_angle = np.degrees(np.arcsin(NA))

# Create the plot
plt.figure(figsize=(8, 6))
plt.plot(theta, acceptance, label='Acceptance Curve')
plt.axvline(x=max_acceptance_angle, color='r', linestyle='--', label=f'Max Acceptance Angle = {max_acceptance_angle:.2f}°')
plt.fill_between(theta, 0, acceptance, where=(theta <= max_acceptance_angle), color='lightblue', alpha=0.5, label='Accepted Light Region')
plt.title("Light Acceptance in Fiber Optic")
plt.xlabel("Angle (degrees)")
plt.ylabel("sin(θ)")
plt.legend()
plt.grid()
plt.show()

Key Features of the Program:

1. Numerical Aperture Calculation: Uses the formula $\text{NA} = \sqrt{n_{\text{core}}^2 - n_{\text{cladding}}^2}$.
2. Visualization: Plots the sine of the angles, with the acceptance region shaded.
3. Maximum Acceptance Angle: Shows the angle beyond which light will not be accepted by the fiber.

How to Use:

1. Copy and paste the code into a Python environment with matplotlib and numpy installed.
2. Run the code to calculate the NA and display the plot.

Would you like further customization of this program or additional details about the calculations?

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5 Related Questions:

1. How does the numerical aperture affect the light-gathering ability of the fiber?
2. What is the relationship between acceptance angle and critical angle in optical fibers?
3. Can this program be extended for multi-mode fibers with different core/cladding configurations?
4. How does the refractive index difference influence fiber performance?
5. How does wavelength affect numerical aperture?

Tip: Ensure your light source is aligned within the maximum acceptance angle for optimal fiber performance!