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.

To determine the maximum entering angle in degrees for total internal reflection to occur, we need to use Snell's law. Snell's law relates the angles and refractive indices of light as it passes through different media.

The formula for Snell's law is:

n1 * sin(theta1) = n2 * sin(theta2)

Where:
- n1 and n2 are the refractive indices of the two media, in this case, air (n1) and glass (n2).
- theta1 is the angle of incidence (measured with respect to the normal) when light passes from air to glass.
- theta2 is the angle of refraction (also measured with respect to the normal) when light passes from glass to air.

In this scenario, we want to find the maximum entering angle, which means the angle of incidence at which total internal reflection just starts to occur. At this point, the angle of refraction (theta2) will be 90 degrees, which means that the light rays are just grazing along the inner surface of the fiber.

Using Snell's law, we can rearrange the formula to solve for theta1:

sin(theta1) = (n2 / n1) * sin(theta2)

Since theta2 is 90 degrees:

sin(theta1) = (n2 / n1) * sin(90)

sin(theta1) = (n2 / n1)

Substituting the given values:
sin(theta1) = (1.50 / 1.00)

Now, to find theta1, we need to take the inverse sine (or arcsine) of both sides of the equation:

theta1 = arcsin(n2 / n1)

Using the given values:
theta1 = arcsin(1.50 / 1.00)

Calculating this in degrees, we find:
theta1 = 41.8 degrees

Therefore, the maximum entering angle for the light ray to pass from air to the glass fiber for total internal reflection to occur is approximately 41.8 degrees.