Calculating Travel Time for Light in an Optical Fiber

[chrisliu1234]

Figure 35-57 shows an optical
fiber in which a central plastic
core of index of refraction n1 
1.58 is surrounded by a plastic
sheath of index of refraction n2 
1.53. Light can travel along different
paths within the central
core, leading to different travel times through the fiber.This causes an
initially short pulse of light to spread as it travels along the fiber,
resulting in information loss. Consider light that travels directly along
the central axis of the fiber and light that is repeatedly reflected at the
critical angle along the core–sheath interface, reflecting from side to
side as it travels down the central core. If the fiber length is 300 m,
what is the difference in the travel times along these two routes?

I know that I need to use t=L/v1=n1*L/c which becomes t=L/v1*cos(theta)=n1*L/(c*sqrt(1-(sin(theta)/n1)^2), but now I am stuck trying to figure the time for the question.

 

[I like Serena]

Figure 35-57 shows an optical
fiber in which a central plastic
core of index of refraction n1 
1.58 is surrounded by a plastic
sheath of index of refraction n2 
1.53. Light can travel along different
paths within the central
core, leading to different travel times through the fiber.This causes an
initially short pulse of light to spread as it travels along the fiber,
resulting in information loss. Consider light that travels directly along
the central axis of the fiber and light that is repeatedly reflected at the
critical angle along the core–sheath interface, reflecting from side to
side as it travels down the central core. If the fiber length is 300 m,
what is the difference in the travel times along these two routes?

I know that I need to use t=L/v1=n1*L/c which becomes t=L/v1*cos(theta)=n1*L/(c*sqrt(1-(sin(theta)/n1)^2), but now I am stuck trying to figure the time for the question.

Hi chrisliu1234! Welcome to MHB! (Smile)

Let's start with $t=\frac{n_1 L}{c}$ for the time to travel along the central axis.
Did you find the corresponding time?

As for the light traveling at critical angles, you're supposed to deduce a formula without theta.
Is that perhaps where your problem is? (Wondering)

 

[chrisliu1234]

Hi chrisliu1234! Welcome to MHB! (Smile)

Let's start with $t=\frac{n_1 L}{c}$ for the time to travel along the central axis.
Did you find the corresponding time?

As for the light traveling at critical angles, you're supposed to deduce a formula without theta.
Is that perhaps where your problem is? (Wondering)

So does change in time = t zigzag - t direct = n1^2*L/n2*c - n1*L/c?

 

[I like Serena]

So does change in time = t zigzag - t direct = n1^2*L/n2*c - n1*L/c?

That looks right yes. (Nod)