Why in fibre optic cable,1310nm or 1550nm wave length is normally chosen for communication of data .?

Above mentioned wavelengths(Gates) are normally used for transmission of datas from generating power station to control room of any sub -station.

Answer:
It is a combination of things.

First you want wavelengths that are not likely to be diffuesed or absorbed to any measurable degree as they propagate. Were this to happen, signals would not propagate as far.

Second you need to distinguish between wavelengths. In dual wavelength applications, send on end A is 1310 nm and receive is 1550 nm and on end B send is 1550 nm and receive is 1310 nm. To keep costs down, an inexpensive light filtering means is used and the two wavelengths need be sufficiently far apart to separate by filtration.

Finaly you need wavelengths that can be easily and inexpensively produced by low cost light sources.

It turns out that these two wavelengths do the job nicely.
820nm is also used in older systems..these are the 'windows' or ranges of wavelength that light can travel easily thru the glass-like material used for the fiber. Other wavelengths are attenuated ( 'blocked').
Because it will send data more fastest than other..it use reflection concept..so if it size more big is very good..than it degree between 2 mirror is very good and widely and make data had send became accurate..
Imbedded in the link below is a chart showing the attenuation characteristics of smf 28 fibre.

Shown are the three basic windows. 850nm, 1310nm and ~1550nm.

You will see that the largest "window" occurs within the 1450nm to 1650nm range. Generally, 1550nm represents a center wavelength. Since multiple wavelengths in the 1500nm to 1600nm range are used in a single fibre for Dense wave devsion multiplexing (DWDM) applications.

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