Light in fibre optic cables Imagine a fibre optic cable stretching from London to New York (5571 km) carrying a data signal
This data signal is split into two parts, red and blue light
Both signals start travelling down the wire at the same time.  Would they reach the other end at the same time? If not, what would be the distance and time delay between the two signals at the other end? (what is the equation to work this out?)
 A: This may seem an simple question, but a truly correct answer is actually a bit more complicated.
This is because there are different speeds and the question is which one is relevant. There is


*

*phase velocity (this is the "ordinary" speed of light, and the one that is described with the refractive index). BUT this is not the speed at which information travels, or even a pulse.

*group velocity. This is the speed a pulse (more specific its envelope) travels. This is much closer to the speed of information 

*front velocity. This is the true speed at which information is traveling (and this cannot be higher than speed of light in vaccuum). This is the speed you are asking for, and in the case of an optical fiber it is very close to the group velocity (which is an easier to work with term than the front velocity).


So the answer, with the refractive index is wrong. It is the group index which is relevant here.
The group index of silica can be found here (http://www.rp-photonics.com/group_index.html).
At 400nm (blue) it is 1.515 and at red 750nm) 1.475. So the time a pulse travels is given by
    $$ L/c_0 \times n_g$$
which is for L=5571km, 28.15 ms for blue vs. 27.41 for red. So red beats blue.
EDIT: I forgot something. Since a fiber is a waveguide, the group velocity is probably still be affected by the special waveguide structure. Graphically this can be understood by imagining, that the light bounces back and forth in the fiber and hence travels a longer path, than given from the physical length of the fiber. This effect depends on the diameter of the fiber core, and is also different for different wavelengths. So the true answer is specific to a special fiber. The above answer is just neglecting this waveguide effects. 
A: light of different frequencies travel at different speeds in matter. this leads to the light reaching the destination at different times. you need to obtain the refractive indices of red and blue light in fibre.
velocity of your light is $v = c/n$, where c is the velocity of light in vacuum, and n is your specific refractive index.
