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

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?

Let the refractive index of a denser medium with respect to a rarer medium be $n_{12}$ and its critical angle be $\theta_C$. At an angle of incidence $A$ when light is travelling from a denser medium to a rarer medium,a part of the light is reflected and the rest is refracted,and the angle between the reflected and refracted rays is $90^o$. Angle $A$ is given by

Three rays of light,namely red $(R)$,green $(G)$ and blue $(B)$ are incident on the face $PQ$ of a right-angled prism $PQR$ as shown in the figure. The refractive indices of the material of the prism for red,green and blue wavelengths are $1.27$,$1.42$ and $1.49$ respectively. The colour of the ray$(s)$ emerging out of the face $PR$ is:

$A$ vertical pencil of rays comes from the bottom of a tank filled with a liquid. When the tank is accelerated horizontally with an acceleration of $7.5\, m/s^2$,the ray is seen to be totally internally reflected by the liquid surface. What is the minimum possible refractive index of the liquid? (Take $g = 10\, m/s^2$)

$A$ ray is incident from a medium of refractive index $2$ into a medium of refractive index $1$. The critical angle is (in $^{\circ}$)