Calculate Time Difference for Two Rays of Light in an Optical Fiber

[raging_hippo]

Ok I've been set the following question:

A piece of optical fibre is 150m long. Two rays of light travel along the fibre. One goes along the axis and the other is reflected off the boundary at the critical angle of 85 degrees. What is the difference in time taken by the two rays.

Speed of light = 3x10^8
Refractive index of core = 1.492



I was wondering if someone could possibly tell me how to find out the time taken by the ray of light that is reflected off the boundary cos i haven't got a clue how to do it

 

[Chen]

Take a look at the attachment. Can you tell what the difference or ratio is between X, the distance that the 'straight' ray travels, and D, the distance that the 'refracting' ray travels? You can, using basic trigonometry. Can you then find out how much longer it takes the 'refracting' ray to travel the same horizontal distance that the 'straight' ray travels?

 

[ShawnD]

That angle is measured from a line perpendicular to the wall of the fibre. When light reflects, the angle of incidence and angle of refraction are the same. Look at this picture to see what's happening
http://myfiles.dyndns.org/math/fibre.jpg

Look at the little triangle I drew on the light ray. V is the speed of the light (n = c/v). Vx is the speed you want, and it looks as if Vx = V sin(85).