**1 Answer**

written 24 months ago by |

**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°.

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.

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