1. The problem statement, all variables and given/known data
I saw this question on this forum

and the answer given

At first I thought that it was obvious why reducing the width of the fibre would reduce the multipath dispersion. But having tried the problem with maths, I'm not so sure.

Can anyone tell me where my maths has gone wrong?

3. The attempt at a solution

I've tried to calculate the maximum possible path difference along a fibre of length l and width d that has a maximim transmission angle of to the normal of the core cladding boundary [tex]\theta[/tex]. I've come up with an expression for this path difference in terms of the length of the fibre... <Attached are my scribbles> (L is the longest path and [tex]\Delta[/tex]L is the greatest possible path difference.)

The problem with this is that the maximum path difference is independant of the width of the fibre and depends only on the angle..