Optical Path length in core fiber of fiber optic faceplate

[jcates7]

Homework Statement

Sorry if this is the wrong section. Please redirect me if there is a more appropriate one.

I'm looking at the timing spread in the time of flight of photons through fibers in a fiber optic faceplate. Essentially the minimum time for photons to propagate through one of the fibers would come from a photon traveling axially through the fiber and not interacting with the fiber walls. The maximum time would come from a photon entering the fiber at the maximum angle allowed within the aperture of the fiber. This photon would undergo total internal reflection along the length of the fiber - producing a longer path length and therefore a longer time to propagate. Hecht describes the path length for a ray not entering orthogonal to the surface normal of one of the fibers to be path length=finber length/cos(transmitted angle). This doesn't physically make sense to me, as it doesn't account for the diameter of the fiber. One can imagine that if the length of the fiber stayed constant and the diameter increased, the path length of rays will increase significantly. This equation doesn't account for this. Could anyone possible shed some light on this?

Thanks,

Josh

Homework Equations

The Attempt at a Solution

 

[Doc Al]

The diameter of the fiber doesn't matter. You know the ray will be reflected multiple times as it travels. So picture the path as a series of zig-zags through the fiber. To find the length of the actual diagonal path, all you need to know is the fiber length and the angle. (And a little trig, of course.)