Path difference in Fibre Optics

In summary, the most direct route for light along a fibre-optic cable with a refractive index of 1.52 and a cladding refractive index of 1.51 is straight down the centre of the cable. To calculate the path difference between two light rays travelling at the critical angle after travelling 10 km of the cable, we first need to calculate the angle of refraction of the light ray using Snell's law. Then, the path difference can be calculated using the difference in the speeds of light in the core and cladding, and the time it takes for the light to travel 10 km. In this case, the path difference is 5.08 km.
  • #1
Graecia
1
0
Hi,
This is a question from a homework which has stumped me:
Light is traveling along a fibre optic cable of refractive index 1.52, the refractive index of the cladding is 1.51 and the critical angle between the two is 82.
a) what is the most direct route for light along the fibre-optic cable
b)The longest route is for light rays traveling at the critical angle. Calculate the path difference between the two rays after travelliing 10km of the cable

I guessed that the most direct route would be straight down the fibre optic cable, and for b i calculated the speed of light in the core to be 1.97x10^8 m/s


Any help would be greatly appreciated,
Many Thanks in advance
 
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  • #2
a) The most direct route for light along the fibre-optic cable is straight down the centre of the cable. This is because light travels faster in the core of the cable than it does in the cladding, so travelling directly down the centre of the cable will give the shortest path.b) To calculate the path difference, you need to first calculate the angle of refraction of the light ray travelling at the critical angle. This can be calculated using Snell's law: n1*sin(θ1) = n2*sin(θ2), where n1 and n2 are the refractive indices of the core and cladding respectively, and θ1 and θ2 are the angles of incidence and refraction respectively. Plugging in the values given, we get: 1.52*sin(82) = 1.51*sin(θ2). Solving for θ2 gives us θ2 = 48.3 degrees, which is the angle of refraction of the light ray travelling at the critical angle. Now we can calculate the path difference between the two rays. The path difference is equal to the difference in the distance travelled by the two rays, which can be calculated using the following equation:Path Difference = (v1 - v2)*t, where v1 and v2 are the speeds of light in the core and cladding respectively, and t is the time taken for the light to travel 10 km. Plugging in the values given, we get: Path Difference = (1.97x10^8 - 1.50x10^8)*(10km/1.97x10^8) = 5.08 km. Therefore, the path difference between the two rays after travelling 10 km of the cable is 5.08 km.
 

FAQ: Path difference in Fibre Optics

1. What is path difference in fibre optics?

Path difference in fibre optics refers to the difference in the distances traveled by two light rays in a fibre optic cable. It is caused by changes in the refractive index of the fibre, which can lead to variations in the speed of light as it travels through the cable.

2. Why is path difference important in fibre optics?

Path difference is important in fibre optics because it can affect the quality and accuracy of the transmitted signal. If the path difference is too large, it can cause signal distortion and loss, resulting in errors and reduced data transmission rates.

3. How is path difference calculated in fibre optics?

Path difference is calculated by measuring the length of the optical path taken by each light ray in the fibre optic cable. This can be done using a variety of methods, including time-of-flight measurements and interferometry techniques.

4. What factors can affect path difference in fibre optics?

There are several factors that can affect path difference in fibre optics, including changes in temperature and pressure, bends or twists in the cable, and imperfections in the fibre itself. These factors can cause variations in the refractive index and lead to path differences.

5. How is path difference managed in fibre optic networks?

To manage path difference in fibre optic networks, various techniques such as dispersion compensation and equalization are used. These methods help to minimize the effects of path difference and ensure reliable and efficient data transmission through the network.

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