Consider the ray diagram for the refraction given below. The maximum value of angle $\theta$ for which the light suffers total internal reflection at the vertical surface is:

The critical angle is $\theta$ for light going from medium $P$ to medium $Q$. If the speed of light in medium $P$ is $V_{P}$,then the speed of light in medium $Q$ is:

$A$ light ray falls on a rectangular glass slab as shown in the figure. If total internal reflection occurs at the vertical face of the slab at point $B$,the refractive index of glass is

$A$ wide slab consisting of two media of refractive indices $n_1$ and $n_2$ is placed in air as shown in the figure. $A$ ray of light is incident from medium $n_1$ to $n_2$ at an angle $\theta$,where $\sin \theta$ is slightly larger than $1/n_1$. Take the refractive index of air as $1$. Which of the following statement$(s)$ is(are) correct?
$(A)$ The light ray enters air if $n_2 = n_1$
$(B)$ The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 < n_1$
$(C)$ The light ray is finally reflected back into the medium of refractive index $n_1$ if $n_2 > n_1$
$(D)$ The light ray is reflected back into the medium of refractive index $n_1$ if $n_2 = 1$

$A$ fish looking up through the water sees the outside world contained in a circular horizon. If the refractive index of water is $\frac{4}{3}$ and the fish is $12 \, cm$ below the surface,the radius of this circle in $cm$ is

The critical angle for light traveling from medium $(i)$ to medium $(ii)$ is $\theta$. If the speed of light in medium $(i)$ is $v$,then the speed of light in medium $(ii)$ is: