The critical angle for a monochromatic light going from medium $A$ to medium $B$ is $\theta$. If the speed of light in medium $A$ is $V$, then the speed of light in medium $B$ is

$A$ diver at a depth of $12 \ m$ in water $(\mu = 4/3)$ sees the sky in a cone of semi-vertical angle:

$A$ planar structure of length $L$ and width $W$ is made of two different optical media of refractive indices $n_1=1.5$ and $n_2=1.44$ as shown in the figure. If $L \gg W$,a ray entering from end $AB$ will emerge from end $CD$ only if the total internal reflection condition is met inside the structure. For $L = 9.6 \ m$,if the incident angle $\theta$ is varied,the maximum time taken by a ray to exit the plane $CD$ is $t \times 10^{-9} \ s$,where $t$ is. . . . . . . [Speed of light $c = 3 \times 10^8 \ m/s$]

Show that for a material with refractive index $\mu \geqslant \sqrt{2}$,light incident at any angle shall be guided along a length perpendicular to the incident face.

$A$ 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 $B$?

$A$ monochromatic beam of light is incident at the interface of two materials of refractive index $n_{1}$ and $n_{2}$ as shown. If $n_{1} > n_{2}$ and $\theta_{C}$ is the critical angle,then which of the following statements is $NOT$ true?