$A$ diver at a depth of $12 \ m$ in water $\left(\mu = \frac{4}{3}\right)$ 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 $c = 3 \times 10^8 \ m/s$]

$A$ small source of light is $4 \ m$ below the surface of a liquid of refractive index $5/3$. In order to cut off all the light coming out of the liquid surface,the minimum diameter of the disc placed on the surface of the liquid is .......... $m$.

The radius of the light circle observed by a fish at a depth of $12 \ m$ is (refractive index of water $\mu = 4/3$):

For the given incident ray as shown in the figure,what is the minimum refractive index of the prism required for total internal reflection of this ray?

In an optical fibre,the core and cladding are made with materials of refractive indices $1.5$ and $1.414$ respectively. To observe total internal reflection,what will be the range of the incident angle with the axis of the optical fibre?