$A$ ray of light travels in the fashion as shown in the figure. After passing through water,the ray grazes along the water-air interface. The value of $\mu_g$ in terms of $i$ is

$A$ ray of light propagates from glass (refractive index $= 3/2$) to water (refractive index $= 4/3$). The value of the critical angle is:

Light travels a distance $x$ in time $t_1$ in air and $10x$ in time $t_2$ in another denser medium. What is the critical angle for this medium?

$A$ point source of light $S$ is placed at the bottom of a vessel containing a liquid of refractive index $\mu = 5/3$. $A$ person is viewing the source from above the surface. There is an opaque disc $D$ of radius $r = 1\, cm$ floating on the surface of the liquid. The centre of the disc lies vertically above the source $S$. The liquid from the vessel is gradually drained out through a tap. The maximum height $h$ of the liquid for which the source cannot be seen at all from above is: (in $, cm$)

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?

$A$ ray of light originates from inside a glass slab and is incident on its inner surface at an angle $\theta$ as shown below. In this experiment,the location $x$ of the spot where the ray hits the screen is recorded. Which of the following correctly shows the plot of variation of $x$ with the angle $\theta$?