To calculate the attenuation of light in an optical fiber over a distance, we can use the formula:

$P(z) = P_0 \times 10^{-\alpha \cdot z / 10}$

where:

• $P(z)$ is the power at distance $z$,
• $P_0$ is the initial power (1 W in this case),
• $\alpha$ is the attenuation constant in dB/km (0.2 dB/km in this case),
• $z$ is the distance in km (1000 km here).

Here's the MATLAB code to calculate the power after attenuation over a 1000 km fiber:

matlabCopy code
% MATLAB program to calculate light attenuation in an optical fiber

% Given data
initial_power = 1; % Initial power in Watts
alpha = 0.2;       % Attenuation constant in dB/km
distance = 1000;   % Distance in km

% Calculate final power using the attenuation formula
final_power = initial_power * 10^(-alpha * distance / 10);

% Display the result
fprintf('The final power after attenuation over %d km is %.10f W\n', distance, final_power);

Explanation of the Code

1. The initial power, attenuation constant, and distance are defined.
2. We apply the attenuation formula to compute the final power after 1000 km.
3. The result is printed to a high precision to observe how much power remains after the large distance.

Would you like a deeper explanation or have further questions on this code?

Here are some follow-up questions that may help extend understanding:

1. What would happen to the final power if the attenuation constant was doubled?
2. How would the final power change over a shorter distance, such as 500 km?
3. What is the effect of initial power on the final result over the same distance?
4. How would attenuation be impacted if the fiber material had a different loss factor?
5. Could this formula be adapted for distances in meters instead of kilometers?

Tip: Attenuation in fiber optics is typically low to allow light to travel long distances, but even small changes in the attenuation constant can have significant effects over large distances.