The figure shows the difference between the refractive index...

Name: Problem 13, Chapter 32: University Physics with Modern Physics
Uploaded: 2022-01-14T01:41:42-08:00
Duration: 4 min 24 s
Channel: Mkhitar Hobosyan
Description: The figure shows the difference between the refractive index profile of a step index fiber and the refractive index profile of a graded index fiber. Applying geometric optics principles, comment on the path followed by a light ray entering each of the optic fibers.

The figure shows the difference between the refractive index profile of a step index fiber and the refractive index profile of a graded index fiber. Applying geometric optics principles, comment on the path followed by a light ray entering each of the optic fibers.

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Key Concepts

Graded-Index Fiber

A graded-index fiber has a core where the refractive index gradually decreases from the center towards the cladding. This continuous variation causes incoming light rays to bend gradually, following a curved, sinusoidal-like trajectory. The smooth bending minimizes abrupt changes in direction, reducing modal dispersion because rays traveling along different paths tend to equalize their transit times.

Geometric Optics Principles

Geometric optics applies the approximation of light as rays, which simplify the analysis of how light propagates through mediums with varying refractive indices. By using laws such as Snell's law and the principle of total internal reflection, one can predict the path of light rays in both step-index and graded-index fibers, explaining how they are confined and guided.

Step-Index Fiber

A step-index fiber features a core with a uniform refractive index sharply bounded by a cladding with a lower index. Light rays entering such a fiber are guided by total internal reflection at the interface between the core and cladding. The rays typically follow a zigzag path as they reflect off the core-cladding boundary, ensuring that the light remains confined in the core.

Transcript

00:01 Hi, we need to understand the difference between the step index optical fiber and graded index optical fiber.

00:08 We have the refraction index profile of the so -called step index fiber and degraded index fiber.

00:17 We need to analyze the light propagation through each of these optical fibers, and we need to understand how the path would be by a light ray that enters each of these two.

00:31 Now, optical fibers work using the principle of the total internal reflection when the light is incident on the boundary of a medium that has a lower index of refraction than the medium in which it is traveling.

00:46 Like in this case, this is optically more dense, let's say, glass.

00:52 Now the incident angle should be greater than the critical angle.

00:57 And let's look at the...

01:00 Here we have a cladding in gray.

01:02 And we have the core which is in blue.

01:06 So you can see that in the first case, in the step index fiber, the refraction index is uniform throughout the whole core.

01:17 So through out the whole core, we have one constant refraction index.

01:22 It is n core.

01:24 And then we have an abrupt change at the lower index of refraction for the cladding.

01:30 In the case of the graded index, fiber we can see here that the refractive index is changing gradually...