6.2 Application of total internal reflection

1.1 Refractive index of light
1.2 Types of medium

2.1 Refraction from a spherical surface

3.1 Shift due to a glass slab
3.2 Lateral Magnification

4.1 Sign convention
4.2 Some important terms
4.3 Ray tracing
4.4 Image formed by covex lens
4.5 Image formed by concave lens

5.1 Thin Lens Formula
5.2 Magnification and Power of lens
5.3 Combination of lenses
5.4 Displacement method to find focal length.
5.5 Silvering of lens

6.1 Critical angle
6.2 Application of total internal reflection

7.1 Dispersive power

8.1 Rainbow

9.1 Spectrometer
9.2 Simple microscope
9.3 Compound microscope
9.4 Astronomical telescope (Refracting type)
9.5 Terrestrial telescope
9.6 Galileo's terrestrial telescope
9.7 Reflecting type telescope

Due to heating of the earth, the refractive index of air near the surface of earth becomes lesser than above it. Light from distant objects reaches the surface of earth with $i > {\theta _c}$, so that the total internal reflection takes place and we see the image of an object along with the object as seen in figure creating an illusion of water near the object.

If $i \geqslant {\theta _c}$ (total internal reflection takes place).

If $i < {\theta _c}$ (refraction takes place and the diver can see the whole world outside).

Using Snell's law,

$$\mu \sin i = \sin r$$

For, $i = {\theta _c}$ (critical angle)

$$r = 90^\circ $$

So, $$\begin{equation} \begin{aligned} \mu \sin {\theta _c} = 1 \\ \sin {\theta _c} = \frac{1}{\mu } \\\end{aligned} \end{equation} $$

From $\Delta AOB$ we can write,

$$\begin{equation} \begin{aligned} \tan i = \frac{r}{d} \\ r = d\tan i \\\end{aligned} \end{equation} $$

So, $$r = \frac{d}{{\sqrt {{\mu ^2} - 1} }}$$