# Speed of light in Fibers

## Speed of light

The speed of light in a vacuum (denoted as $$c$$) is: $$299,792,458$$ metres per second.

### Refractive index

The speed of which light propagates through transparent materials will be is less than $$c$$, by a coefficient called refractive index.

The formula to calculate the speed given a refractive index (called $$n$$) is: $$v = c/n$$.

Air (at standard temperature and pressure) has a refractive index of $$1.000273$$, meaning that light can only travel at $$\approx 299,710,637m/s$$ which is $$\approx 82km/s$$ slower than $$c$$.

## Optical fibers

Fibers are made from the following materials: Silica, Fluoride glass, Phosphate glass and Chalcogenide glass. Their respective refractive index are 1.458, 1.51, 1.701 and unknown. Note that I can’t guarantee that these measurements were done in the same conditions.

These materials range from $$\approx 94,173km/s$$ to $$\approx 123,548km/s$$ slower than $$c$$, or approximately $$\approx 2/3$$ of $$c$$.

### Repeater

Optical fibers over a long distance need to be repeated every few 100km to combat light attenuation. Near-infrared wavelengths are generally used because this wavelength has the lowest attenuation rate.

Note that each repeaters require power which is routed through the cable.

## Apollo example

Apollo transatlantic submarine cable system (now owned by Vodafone).

Based on submarinenetworks.com the Apollo cable network uses Alcatel-Lucent’s 1620 Light Manager (LM).

It supports WDM but for the sake of example let’s only consider the band 2:

• Frequency: $$195.3125 GHz$$
• Wavelength: $$1534.937 nm$$

I have no idea what type of fiber Apollo uses but let’s use Corning® SMF-28® as an example. Which with a wavelength of $$1550 nm$$ has a refractive index of $$1.4682$$.

One particular path called Apollo South has a length of $$\approx 5,582km$$.

The maximum theoretical speed is $$\approx 204,190,477m/s$$ (again, approximately $$\approx 2/3$$ of $$c$$), it takes $$~27ms$$ for the light to cross the ocean. This is excluding any light repeaters or network equipment on the way.

As a side note, it’s possible to communicate between similiar distances closer to $$c$$ using various radio frequencies, as the radio waves travel through air instead of fibers.