Trapped light

Classical Mechanics Level 4

Optical fibers are devices used for guiding light in many applications, most notably for fast communication. A fiber consists of a glass cylinder surrounded by a wall covered in a special coating. The fibers work on a principle called total internal reflection: light enters the fiber at an angle such that it does not get transmitted through the wall of the fiber when it hits the inside of the wall. Therefore, the refraction index of the glass part of the fiber has to be higher than that of its coating.

What is the maximum entering angle in degrees a light ray can pass from the air to the glass fiber for the total internal reflection to occur?

Details and assumptions

  • Measure the entering angle from the axis of the fiber.
  • Use the following refraction indexes: \(n_{\text{air}} = 1.00\), \(n_{\text{glass}} = 1.50\) and \(n_{\text{coating}} = 1.46\).

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