For a light ray to undergo total internal reflection, light must travel from $(i = \text{angle of incidence}, i_C = \text{critical angle})$

The figure shows a transparent block of side lengths $a$ and $a$. The third dimension of the block is negligible. $A$ point source $S$,which can emit light in all directions,can move inside the block. It is desired that no light from $S$ should pass through the segment $AB$. The region in which $S$ must be present to satisfy this condition is shown by the shaded region. Choose the correct option.

The wavelengths of light in two liquids $x$ and $y$ are $3500 \, \mathring{A}$ and $7000 \, \mathring{A}$ respectively. The critical angle of $x$ with respect to $y$ is .......... $^o$.

$A$ water-proof laser pointer of length $10 \,cm$ is placed in a water tank. It rotates about a horizontal axis passing through its centre of mass in a vertical plane as shown in the figure. The time period of rotation is $60 \,s$. Assuming the water to be still and no reflections from the surface of the tank, the duration for which the light beam escapes the tank in one time period is close to ............. $s$. (Take, refractive index of water $= 1.33$)

$A$ 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 $c = 3 \times 10^8 \ m/s$]

$A$ fish inside water sees the outside world through a circular horizon. If the refractive index of water is $4/3$ and the fish is $12 \, cm$ below the water surface,then the radius of this circle is $= ..... cm$.