The speed of light in media $M_1$ and $M_2$ are $1.5 \times 10^8 \ m/s$ and $2.0 \times 10^8 \ m/s$ respectively. $A$ ray of light enters from medium $M_1$ to $M_2$ at an incidence angle $i$. If the ray suffers total internal reflection,the value of $i$ is

Which of the following is used in optical fibres?

$A$ diver looking up through the water sees the outside world contained in a circular horizon. The refractive index of water is $\frac{4}{3}$,and the diver's eyes are $15 \, cm$ below the surface of water. Then the radius of the circle is

$A$ ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\theta$ as shown below. In this experiment,the location $x$ of the spot where the ray hits the screen is recorded. Which of the following correctly shows the plot of variation of $x$ with the angle $\theta$?

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

Consider a glass prism immersed in a liquid as shown below. The refractive index of glass and liquid is $1.5$ and $1.2$,respectively. $A$ ray of light enters the prism perpendicular to the face $AB$. If the ray is totally internally reflected at the face $AC$,then the largest value of angle $\theta$ is: