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Explain total internal reflection in fibre optics
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Solution:

Internal Reflection:

  • When a ray of light passes from a denser to a rarer medium, it is bent away from the normal.

  • When the angle of incidence is gradually increased, the corresponding angle of refraction also increases.

  • At a particular angle of incidence, the angle of retraction reaches to 90°.

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  • That particular value of angle of incidence is called the critical angle of the medium.

  • When the angle of incidence is further increased above the critical angle, the ray is totally reflected back in the same denser medium itself.

  • This phenomenon is called total internal reflection. Two conditions are to be satisfied for total internal reflection.

  • 1) Light should travel from denser medium to rarer medium.

  • 2) The angle of incidence should be greater than the critical angle of the medium.

  • According to Snell's law,

$$ \mu_{\mathrm{r}}{ }^{\mathrm{d}}=\frac{\operatorname{Sin} \mathrm{i}}{\operatorname{Sin} \mathrm{r}} \\ $$

The refractive index of the rarer medium with respect to denser medium,

$$ \mu_{\mathrm{d}}{ }^{\mathrm{r}}=\frac{\operatorname{Sin} \mathrm{r}}{\operatorname{Sin} \mathrm{i}} \\ $$

Also, the refractive index of the denser medium with respect to rare medium In critical angle position, $\mathrm{i}=\mathrm{c}$ and $\mathrm{r}=90^{\circ} \\$ $$ \begin{aligned} &\therefore \mu_{\mathrm{d}}{ }^{\mathrm{r}}=\frac{\operatorname{Sin} \mathrm{r}}{\operatorname{Sin} \mathrm{i}}=\frac{\operatorname{Sin} 90^{\circ}}{\operatorname{Sin} \mathrm{c}} \\ &\text { i.e., } \mu_{\mathrm{d}}{ }^{\mathrm{r}}=\frac{1}{\operatorname{Sin} \mathrm{C}}\left(\because \operatorname{Sin} 90^{\circ}=1\right) \end{aligned} \ $$

The sparkling of the diamond, the phenomenon of mirage and the propagation of light waves along optical fibre are due to the total internal reflection.

$$ \begin{array}{|c|l|c|c|} \hline \text { Sl.No. } & {\text { Medium }} & \begin{array}{c} \text { Refractive index } \\ \mu \text { w.r.t air } \end{array} & \text { Critical angle : C } \\ \hline 1 & \text { Water } & 1.33 & 48^{\circ} 45^{\prime} \\ \hline 2 & \text { Glass } & 1.5 & 41^{\circ} 48^{\prime} \\ \hline 3 & \text { Diamond } & 2.42 & 24^{\circ} 24^{\prime} \\ \hline \end{array} $$

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