JEE Main & Advanced Physics Communication System / संचार तंत्र Optical Fibre

The optical fibres are used to transmit light signals from one place to another without any practical loss in the intensity of light signal.

(1) Design : Optical fibre is made of a thin glass core (diameter 10 to 100 \[\mu m\]) surrounded by a glass coating called cladding are protected by a jacket of plastic.

(2) Principle : It works on the principle of total internal reflection.

(3) Action : The refractive index of the glass used for making core \[({{\mu }_{1}}\approx 1.7)\] is a little more than the refractive index of the glass \[({{\mu }_{1}}\approx 1.5)\] used for making the cladding i.e. \[{{\mu }_{1}}>{{\mu }_{1}}\].

The core dimension is so small \[(\approx 10\,mm)\] that the light entering will almost essentially be having incident angle \[({{\theta }_{i}})\] more than the critical angle \[({{\theta }_{c}})\] and will suffer total internal reflection at the core. Cladding boundary such successive total reflections at opposite boundaries will confine the light to the core as shown in figure.

(4) Critical angle \[({{\theta }_{c}})\]: At core-cladding interface if \[\theta ={{\theta }_{c}}\] then \[\cos {{\theta }_{c}}=\frac{\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}}{{{\mu }_{1}}}\]\[\Rightarrow \]\[{{\theta }_{c}}={{\cos }^{-1}}\left( \frac{\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}}{{{\mu }_{1}}} \right)\]

(5) Acceptance angle \[({{\theta }_{a}})\] : The value of maximum angle of incidence with the axis of fibre in air for which all the incident light is totally reflected is known as acceptance angle.

If \[{{\theta }_{a}}=\] Acceptance angle then  \[{{\mu }_{1}}=\] refractive index of core, \[{{\mu }_{2}}=\] refractive index of cladding. \[\sin {{\theta }_{a}}=\frac{\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}}{{{\mu }_{0}}}\]\[\Rightarrow \]\[{{\theta }_{a}}={{\sin }^{-1}}\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}\] (for air \[{{\mu }_{0}}=1\])

(6) Numerical aperture : Light gathering capability of a fibre is related to numerical aperture. This is defined as the sine of acceptance angle i.e. \[NA=\sin i=\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}\]

The numerical aperture can also be given in terms of relative core-cladding index difference \[(\Delta )\], where \[\Delta =\frac{\mu _{1}^{2}-\mu _{2}^{2}}{2\mu _{1}^{2}}\]

Thus, \[NA=\sqrt{\mu _{1}^{2}-\mu _{2}^{2}}={{\mu }_{1}}\sqrt{2\Delta }\]

(7) Fibre attenuation : In practice a very small part of light energy is lost from an optical fibre. This reduction in energy of the light is called attenuation and is described by \[I={{I}_{0}}{{e}^{-\alpha x}}\] 

where \[{{I}_{0}}=\] Intensity of light when it enters the fibre

\[I=\] Intensity of light at a distance x along the fibre

\[\alpha =\] Absorption co-efficient or attenuation co-efficient

Also attenuation (in dB) \[=10{{\log }_{10}}\frac{I}{{{I}_{0}}}\]

(8) Types of optical fibre

(i) Monomode optical fibre : It has a very narrow core of diameter about \[5\,\mu m\] or less, cladding is relatively big.

(ii) Multimode optical fibre : It is again of two types

(a) Step index multimode fibre :

The diameter of the core is about  \[50\,\mu m\] 

Core has constant R.I \[{{\mu }_{1}}\] from it's centre to boundary.

The refractive index then changes to a lower value of \[{{\mu }_{2}}\], which remains constant through the cladding.

Since refractive index of a material depend on the wavelength of light. The wavelength fellow diff. paths.

The overall time difference between two wavelengths reaches the other end is of the order of \[33\times {{10}^{-9}}\] sec/cm length of the fibre.

(iii) Graded index multimode fibre : Refractive index decreases smoothly from it's centre to the outer surface of the fibre (cladding). There is no notieable boundary between core and cladding.