Digital information that is transmitted along optic fibres is often subject to dispersion due to light taking different paths along the fibre.

In a particular optic fibre of length 2.00×10⁴ m, the refractive index of the cladding is 1.41 and that of the core is 1.44.

Two possible light paths are:

Path A: along the central axis of the fibre.
Path B: the path followed by light that is initially incident on the cladding at an angle just greater than the critical angle.

The speed of light in the core of the fibre is 2.10×10⁸ ms^–1.

Show that the difference in transmission time between path B and path A is approximately 2.0 μs.

ratio of \(n = \frac{{1.41}}{{1.44}}\left( { = 0.979} \right)\);
path difference between B and A\( = 2.00 \times {10^4} - \frac{{2.00 \times {{10}^4}}}{{0.979}} = 4.00 \times {10^2}\left( {\rm{m}} \right)\);
time difference\( = \frac{{4.00 \times {{10}^2}}}{{2.10 \times {{10}^8}}}\);
≈2.00×10^–6s