A light ray in the core (n=1.40) of a cylindrical optical...

A light ray in the core $(n=1.40)$ of a cylindrical optical fiber is incident on the cladding. See the figure with Problem $14 .$ A ray is transmitted through the cladding $(n=1.20)$ and into the air. The emerging ray makes an angle $\theta_{2}=5.00^{\circ}$ with the outside surface of the cladding. What angle $\theta_{1}$ did the rav in the core make with the axis?

Key Concepts

Refractive Index

The refractive index is a measure of how much a material slows down light compared to vacuum, and it determines the degree of bending (refraction) when light transitions between materials. In the context of optical fibers, different refractive indices of the core, cladding, and external medium set the conditions for light confinement and transmission, and they are key parameters in applying Snell's Law to compute the propagation angles.

Snell's Law

Snell's Law is the fundamental principle governing the refraction of light as it passes from one medium to another. It states that the product of the refractive index of a medium and the sine of the angle of incidence in that medium is equal to the product of the refractive index of the second medium and the sine of the angle of refraction. This relationship is essential when analyzing how light rays change direction at interfaces, such as from the fiber core to the cladding or from the cladding to air.

Geometrical Optics in Optical Fibers

Geometrical optics in optical fibers involves tracing the paths of light rays as they propagate through the fiber. This includes understanding how the angle that a light ray makes with the fiber axis relates to its incidence at the core-cladding interface and the subsequent refraction processes. Knowledge of this concept is crucial for analyzing the guiding conditions and the efficiency of light transmission in optical fibers.

Transcript

00:01 A fiber is a transparent material like plastic that has been extruded into a long cable.

00:09 Usually there are two parts to the fiber.

00:17 One, the inner part is called the core, and that is where you would like the ray to get caught.

00:24 And the cladding usually has a lower index of refraction and is there to help guide the ray inside of the core.

00:35 Here, this is a little bit unusual, so we have a ray coming in from outside, going through the cladding and the core and coming out the other side.

00:48 What's different about this is that we're out in the air on exit, and the angle that is given is with respect to the surface when we want the angle with respect to the normal if we are going to use snell's law.

01:07 So i will write snell's law down that n2 sine of theta 2, and we'll call it phi 2, just for distinguishing it, is equal to the n inside the cladding times the sign of the angle inside of the cladding.

01:32 And here, we just want to be careful, to show that phi 2 is with respect to the normal on exit.

01:46 So remember that snell's law is written for angles with respect to normal, not to the surface itself.

02:06 There is a good reason for that, and it has to do with curved surfaces, which this is not really a very good example of that, but in this case, our phi 2 is going to be 90 degrees minus 5 degrees or 85.

02:32 And so we have 1 times sign of 85 is equal to the end of the cladding, which is 1 .20.

02:42 And the angle that we're looking for is inside with respect to the normal.

02:50 And we'll try to show that theta cladding.

02:57 And we can then find that out by taking inverse sign.

03:08 We wind up with that theta cladding is 56 .1 degrees.

03:23 We'll say 1 .12 degrees.

03:27 Keep it to one extra significant figure.

03:30 And then what we can do is we can find the anchors.

03:35 To the normal inside the core...