A particular optical fiber consists of a cylindrical \"core\" (n = 1.60) surroun

Question

A particular optical fiber consists of a cylindrical "core" (n = 1.60) surrounded by a concentric cylindrical jacket called the "cladding" (n = 1.50). The cladding, in turn, is surrounded by air (n = 1.00). An incoming ray of light has an angle a to the central axis of the core, as shown.

a. For what range of angles for a will the ray experience total internal reflection at the core-cladding interface?

b. For what range of angles for a will the ray pass through both the core-cladding interface and the

cladding-air interface (thereby escaping from the upper edge of the cladding into the air)?

c. Suppose that a very long bundle of many optical fibers just like the one above is laid along the ocean floor. Pulses of light are sent through the fibers to carry telephone conversations and Internet data from California to Hawaii. How much time does it take light entering one end of a 2550-mile-long fiber to reach the other end? (Assume that the ray enters the above optical fiber exactly on the central axis of the core ((a = 0 degrees) and that the fiber is perfectly straight.) (Hint: What is the speed of light inside the core?)

Please show your work, and explain the steps.

A particular optical fiber consists of a cylindrical "core" (n = 1.60) surrounded by a concentric cylindrical jacket called the "cladding" (n = 1.50). The cladding, in turn, is surrounded by air (n = 1.00). An incoming ray of light has an angle a to the central axis of the core, as shown. For what range of angles for a will the ray experience total internal reflection at the core-cladding interface? For what range of angles for a will the ray pass through both the core-cladding interface and the cladding-air interface (thereby escaping from the upper edge of the cladding into the air)? Suppose that a very long bundle of many optical fibers just like the one above is laid along the ocean floor. Pulses of light are sent through the fibers to carry telephone conversations and Internet data from California to Hawaii. How much time does it take light entering one end of a 2550-mile-long fiber to reach the other end? (Assume that the ray enters the above optical fiber exactly on the central axis of the core ((a = 0 degrees) and that the fiber is perfectly straight.) (Hint: What is the speed of light inside the core?)

Explanation / Answer

a)

incident angle, i = 90 - alfa

sin(i)/sin(r) = n2/n1

here r = 90 degrees

sin(90-alfa) = 1.5/1.6

cos(alfa) = 0.9375

alfa = 20.36 degrees


so alfa should be lower than 20.36 degrees

b)

sin(i)/sin(r) = n2/n1 at core cladding intereface

sin(90-alfa)/sin(r) = n2/n1 --(1)


sin(theta_i)/sin(theta_r) = n3/n2 at cladding and air intereface

sin(r)/sin(90) = n3/n2 --(2)

multiply eqns 1 and 2

sin(90-alfa)/sin(90) = n3/n1

cos(alfa) = n3/n1

alfa = cos^-1(1/1.6)

alfa = 51.32 degrees

c) v = c/n = 3*10^8/1.6 = 1.875*10^8 m/s

d = 2550*1.607*1000 = 4097850 m

t = d/v

= 4097850/(1.875*10^8)

= 0.0218552 s

= 21.855 m s

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