The speed of light in media ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ is $1.5\times {10}^8$ $\mathrm{m}/\mathrm{s}$ and $2.0\times {10}^8$ $\mathrm{m}/\mathrm{s}$ respectively. A ray of light enters from medium ${\mathrm{M}}_1$ to ${\mathrm{M}}_2$ at an incidence angle i. If the ray suffers total internal reflection, the value of i is:

The ratio of the velocity of light in a medium to the velocity of light in a vacuum is \(\frac{4}{5}\). If the ray of light is emerging from this medium into the air, then the critical angle for this interface of medium and air will be:

A rainbow is formed due to:

Light enters at an angle of incidence in a transparent rod of refractive index n. For what value of the refractive index of the material of the rod, will the light, once entered into it, not leave it through its lateral face whatsoever be the value of the angle of incidence?
1. $n$ $>\sqrt{2}$
2. 1.0
3. 1.3
4. 1.4

In total internal reflection when the angle of incidence is equal to the critical angle for the pair of media in contact, what will be the angle of refraction?

If \(C_1,~C_2 ~\mathrm{and}~C_3\) are the critical angle of glass-air interface for red, violet and yellow color, then:

A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ}\), then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where:
1. \(\theta = 49^{\circ}\)$$
2. \(\theta = 90^{\circ}\)$$
3. \(\theta = 98^{\circ}\)$\mathrm{}$
4. \(\theta = 24\frac{1}{2}^{\circ}\)$$

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels up, to the surface of the liquid and moves along its surface (see figure). 
                
How fast is the light traveling in the liquid?

A rod of glass ($\mu$ = 1.5) and of the square cross-section is bent into the shape as shown. A parallel beam of light falls on the plane flat surface A as shown in the figure. If d is the width of a side and R is the radius of a circular arc then for what maximum value of $\frac{d}{R}$, light entering the glass slab through surface A will emerge from the glass through B?

For the given incident ray as shown in the figure, in the condition of the total internal reflection of this ray, the minimum refractive index of the prism will be:

1. $\frac{\sqrt{3}+1}{2}$

2. $\frac{\sqrt{2}+1}{2}$

3. $\sqrt{\frac{3}{2}}$

4. $\sqrt{\frac{7}{6}}$