A cylindrical vessel of diameter $12 \mathrm{cm}$ contains $800\mathrm{\pi } {\mathrm{cm}}^3$ of water. A cylindrical glass piece of diameter $8.0 \mathrm{cm}$ and height $8.0 \mathrm{cm}$ is placed in the vessel. If the bottom of the vessel under the glass piece is seen by the paraxial rays (see figure), locate its image. The index of refraction of glass is $1.50$ and that of water is$1.33$.

Consider the situation in the figure. The bottom of the pot is a reflecting plane mirror. $S$is a small fish and $T$is a human eye. The refractive index of water is $\mu \mathit{.}$
(a) At what distance(s) from itself will the fish see the image(s) of the eye?
(b) At what distance(s) from itself will the eye see the image(s) of the fish?

A small object is placed at the center of the bottom of a cylindrical vessel of radius $3 \mathrm{cm}$ and height $4 \mathrm{cm}$ filled completely with water. Consider the ray leaving the vessel through a corner. Suppose this ray and the ray along the axis of the vessel are used to trace the image. Find the apparent depth of the image and the ratio of real depth to the apparent depth under the assumptions taken. Refractive index of water $=1.33.$

A cylindrical vessel whose diameter and height both are equal to $30 \mathrm{cm}$ is placed on a horizontal surface and a small particle $P$ is placed in it at a distance of $5.0 \mathrm{cm}$ from the center. An eye is placed at a position such that the edge of the bottom is just visible (see figure). The particle $P$is in the plane of the drawing. Up to what minimum height should water be poured in the vessel to make the particle $P$ visible?

A light ray is incident normally on the face $AB$ of a right-angled prism $ABC (\mathrm{\mu }=1.50)$ as shown in the figure. What is the largest angle $\varphi$ for which the light ray is totally reflected at the surface $AC$?