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: nair=1.00 , nglass=1.50 and ncoating=1.46
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To determine the maximum entering angle for total internal reflection in the glass fiber, we can use Snell's law and the concept of critical angle.
Snell's law relates the angles and indices of refraction of two media:
n1 * sin(theta1) = n2 * sin(theta2)
Where:
- n1 and n2 are the indices of refraction of the two media
- theta1 and theta2 are the angles between the ray and the normal to the surface in the respective media
For total internal reflection to occur, the light ray must be incident on the interface between the glass and the surrounding media (air or coating) with an angle greater than the critical angle. The critical angle (theta_c) can be found by setting theta2 to 90 degrees:
n1 * sin(theta_c) = n2
In this case, the glass is medium 1 (nglass) and the surrounding medium is air (nair). Therefore, we can substitute these values into the equation:
nglass * sin(theta_c) = nair
Now, we can solve for theta_c:
sin(theta_c) = nair / nglass
theta_c = arcsin(nair / nglass)
Using the given values nair=1.00 and nglass=1.50, we can calculate the critical angle:
theta_c = arcsin(1.00 / 1.50)
theta_c ≈ 41.8 degrees
Therefore, the maximum entering angle for the light ray from air to the glass fiber is approximately 41.8 degrees.