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.
![](/upload/html_folder/22_Optical_Fibre/22_Optical_Fibre_files/image002.png)
(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.
![](/upload/html_folder/22_Optical_Fibre/22_Optical_Fibre_files/image009.png)
(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.
![](/upload/html_folder/22_Optical_Fibre/22_Optical_Fibre_files/image015.png)
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.
![](/upload/html_folder/22_Optical_Fibre/22_Optical_Fibre_files/image031.png)
(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.
![](/upload/html_folder/22_Optical_Fibre/22_Optical_Fibre_files/image035.png)
Since refractive index of a material depend on the wavelength of light. The wavelength
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