If the critical angle for total internal reflection from a medium to vacuum is $45^{\circ}$,then the velocity of light in the medium is,

$A$ glass prism of refractive index $1.5$ is immersed in water (refractive index $\frac{4}{3}$) as shown in the figure. $A$ light beam incident normally on the face $AB$ is totally internally reflected at the face $AC$ to reach the face $BC$,if:

Consider a glass cube slab of dielectric bound by the planes $x=0, x=a$; $y=0, y=b$; $z=0, z=c$; with $b > a > c$. The slab is placed in air and has a refractive index of $n$. The minimum value for $n$,such that all rays entering the dielectric at $y=0$ reach $y=b$ is

$A$ point source of light is placed $4 \; m$ below the surface of water of refractive index $5/3$. The minimum diameter of a disc which should be placed over the source on the surface of water to cut-off all light coming out of water is ... $m$.

Brilliance of diamond is due to

$A$ parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R=0.05 \ m$ and refractive index $n=1.5$, placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose nearest distance $x$ from the cylinder is