At what angle of incidence should a ray be incident on a glass sphere of refractive index $3/2$ so that the ray does not emerge from the sphere?

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 .......... $^o$.

Material $A$ has a critical angle ${i_A},$ and material $B$ has a critical angle ${i_B}$ $({i_B} > {i_A})$. Then which of the following is true?
$(i)$ Light can be totally internally reflected when it passes from $B$ to $A$.
$(ii)$ Light can be totally internally reflected when it passes from $A$ to $B$.
$(iii)$ The critical angle for total internal reflection is ${i_B} - {i_A}$.
$(iv)$ The critical angle between $A$ and $B$ is ${\sin ^{ - 1}}\left( {\frac{{\sin {i_A}}}{{\sin {i_B}}}} \right)$.

$A$ ray of light enters from a rarer to a denser medium. The angle of incidence is $i$. Then the reflected and refracted rays are mutually perpendicular to each other. The critical angle for the pair of media is

$A$ beam of light consisting of red,green and blue colours is incident on a right-angled prism. The refractive index of the material of the prism for the above red,green and blue wavelengths are $1.39, 1.44$ and $1.47$ respectively.
The prism will

Rays from a point source of light situated at height $h$ below the liquid surface having refractive index $\mu$,form a circular patch of light of radius $r$ on the surface. The area of the patch is