$A$ ray of light enters from air into water. Which of the following figures shows the dispersion of light?

Which of the following could not produce a virtual image?

In the figure shown,consider the first reflection at the plane mirror and the second at the convex mirror. $AB$ is the object.

As shown in the figure, a parallel beam of light is incident on the upper part of a prism of angle $1.8^{\circ}$ and material of refractive index $1.5$. The light emerging from the prism falls on a concave mirror of radius of curvature $40 \,cm$. The distance of the point from the principal axis of the mirror where the light rays are focused after reflection from the mirror is:

Ray optics is valid when characteristic dimensions are:

$A$ beaker of radius $r$ is filled with water (refractive index $\frac{4}{3}$) up to a height $H$ as shown in the figure. The beaker is kept on a horizontal table rotating with angular speed $\omega$. This makes the water surface curved so that the difference in the height of the water level at the center and at the circumference of the beaker is $h$ $(h \ll H, h \ll r)$,as shown in the figure. Take this surface to be approximately spherical with a radius of curvature $R$. Which of the following is/are correct? ($g$ is the acceleration due to gravity)
$(A)$ $R=\frac{h^2+r^2}{2 h}$
$(B)$ $R=\frac{r^2}{2 h}$
$(C)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{4}\left(1+\frac{\omega^2 H}{4 g}\right)^{-1}$
$(D)$ Apparent depth of the bottom of the beaker is close to $\frac{3 H}{2}\left(1+\frac{\omega^2 H}{2 g}\right)^{-1}$