$A$ ray of light falls on a transparent glass slab with a refractive index (relative to air) of $1.62$. The angle of incidence for which the reflected and refracted rays are mutually perpendicular is

$A$ ray of light is incident at the glass-water interface at an angle $i$. It emerges finally parallel to the surface of water. Then the value of refractive index of glass,${\mu _g}$,is:

If ${ }_{i} \mu_{j}$ represents the refractive index when a ray goes from medium $i$ to medium $j$,then the product ${ }_2 \mu_1 \times { }_3 \mu_2 \times { }_4 \mu_3$ is equal to:

An observer can see the top of a thin rod of height $h$ through a pinhole. The height of the container is $3h$ and its radius is $2h$. When the container is filled with a liquid up to a height of $2h$,the observer can see the bottom end of the rod. Find the refractive index of the liquid.

Let the $x-z$ plane be the boundary between two transparent media. Medium $1$ in $z \ge 0$ has a refractive index of $\sqrt{2}$ and medium $2$ with $z < 0$ has a refractive index of $\sqrt{3}$. $A$ ray of light in medium $1$ given by the vector $\overrightarrow{A} = 6\sqrt{3} \widehat{i} + 8\sqrt{3} \widehat{j} - 10\widehat{k}$ is incident on the plane of separation. The angle of refraction in medium $2$ is ......$^o$.

Draw a figure that illustrates the reflection and refraction of light.