(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A glass optical fibre of length L = 3.2 m is in a medium of glycerine with a refractive index n0 = 1.47 . The fibre has a core of refractive index, n_{1}= 1.58 and diameter, d = 100μm surrounded by a thin cladding of refractive index, n_{2}= 1.53. The end of the fibre is cut square (see diagram).

[PLAIN]http://img69.imageshack.us/img69/4976/imagenz.gif [Broken]

For the aforementioned fibre, what is the total path length of a ray within the fibre that enters the fibre at the acceptance angle?

3. The attempt at a solution

Here are the stuff that I have already calculated:

* The minimum angle, θ_{2}, for total internal reflection at the core/cladding boundary: 75.5 degrees.

* The angle, θ_{1}, to the axis of the fibre that corresponds to the minimum angle, θ_{2}: 14.5 degrees.

* The acceptance angle θ_{0}: 15.6 degrees.

So, now to find the path length of a ray within the fibre that enters the fibre at the acceptance angle I tried using trigonometry:

Since d=100.0 μm = 100 x 10^{6}m. We have d/2 = 50 x 10^{6}.

[tex]sin (14.5) = \frac{50 \times 10^6}{x}[/tex]

x= a very huge number!!

But the answer must be 3.305 m! What did I do wrong?

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# Homework Help: Path length of a light ray

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