Suppose the fiber depicted in Figure 26-75 has an index of...

Suppose the fiber depicted in Figure $26-75$ has an index of refraction of 1.62 and its curved surface is surrounded by a cladding material with an index of refraction of $1.52 .$ (a) What is the critical angle for total internal reflection of rays at the fibercladding boundary? (b) What is the maximum angle $\theta_{\text { at }}$ which rays can enter the fiber from air as shown and undergo total internal reflections (c) If the diameter of the fiber core is $9.0 \mu \mathrm{m},$ how many reflections per meter does the ray undergo when it arrives at the boundary at the critical angle?

Suppose the fiber depicted in Figure $26-75$ has an index of refraction of 1.62 and its curved surface is surrounded by a cladding material with an index of refraction of $1.52 .$ (a) What is the
critical angle for total internal reflection of rays at the fibercladding boundary? (b) What is the maximum angle $\theta_{\text { at }}$ which rays can enter the fiber from air as shown and undergo total internal reflections (c) If the diameter of the fiber core is $9.0 \mu \mathrm{m},$ how
many reflections per meter does the ray undergo when it arrives at
the boundary at the critical angle?

Key Concepts

Acceptance Angle

The acceptance angle is the maximum angle at which incoming light from an external medium (such as air) can enter an optical fiber and continue to be propagated by total internal reflection. This concept is crucial for characterizing the light-gathering efficiency and coupling of optical fibers.

Snell's Law

Snell's Law describes how light bends when passing from one medium to another with different indices of refraction. It relates the sine of the incident angle to the sine of the refracted angle, providing the theoretical basis for determining the critical angle when the refracted angle reaches 90 degrees.

Total Internal Reflection

Total internal reflection is the phenomenon where light, travelling in a medium with a higher index of refraction, strikes the boundary with a lower-index medium at an angle greater than the critical angle, resulting in complete reflection back into the original medium. This is the principle that allows optical fibers to confine light effectively.

Index of Refraction

The index of refraction is a dimensionless number that describes how light propagates through a medium. It quantifies the reduction in the speed of light compared to its speed in a vacuum and is central to understanding how light bends or slows down when entering different materials.

Critical Angle

The critical angle is the smallest angle of incidence for which total internal reflection occurs at the interface between two media. It is determined by the ratio of the indices of refraction of the two media and is essential for designing systems like optical fibers, where light must be confined within the core.

Transcript

00:01 In this question, we have a fibro optic.

00:03 The fibro optic has an index of refraction of 1 .62, and then there's a cladding material surrounding the fibro optic and the refractive index is 1 .52.

00:21 And so we need to, there are three parts in this question.

00:28 In part a, we want to find a critical angle for total internal reflection to take place.

00:32 So to do this, okay, we'll be using snail's law and then at critical angle.

00:53 The angle in the cladding is from the normal is 90 degrees.

01:00 So we have n fiber, sine data is equal to n clad.

01:11 Side data clad okay so sign 90 degrees is one so sign i decide data is equal to n clad divided by n bival it's equal to 1 .52 divided by 1 .62 this is equal to 0 .938 and so data for total internal reflection is equal to 69 .8 degrees okay so this is this is our critical angle.

01:47 So this is the answer for part a.

01:54 In part b, we want to find a maximum angle of incidence.

01:59 So that total internal reflection can take place.

02:03 So from the diagram, this is our data r from the incidence angle.

02:17 So when you look at this right angle, triangle here, so data r is 90 degrees minus data c.

02:30 This is 20 .2 degrees and so data c is the smallest angle for total internal reflection okay so data r is the largest angle of reflection okay, and the corresponding data i, a, the angle of incidence will be the largest.

03:33 Okay, so we are going to use 20 .2 to calculate our data i.

03:41 So, and fiverr is equal to sign data i, diva right, side, data, r.

03:49 Okay, this is now slow again.

03:51 And so, uh, okay, which means that side data i is equal to n fiber sign data r okay so putting the numbers equal to 1 .62 times sign 20 .2 degrees and you get 0 .560 and so data i is equal to 34 34 .1 degrees okay so this is the answer for part b.

04:38 Okay then in part c, you want to find a number of reflections per meter if the diameter of the fiber core is 9 micrometer...

Please give Ace some feedback