Three identical convex lenses each of focal length $f$ are placed in a straight line separated by a distance $f$ from each other. An object is located at $f/2$ in front of the leftmost lens. Then,

$A$ 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 $\frac{3 H}{2}\left(1+\frac{\omega^2 H}{2 g}\right)^{-1}$

Which one of the following spherical lenses does not exhibit dispersion? The radii of curvature of the surfaces of the lenses are as given in the diagrams.

$A$ finite size object is placed normal to the principal axis at a distance of $30 \ cm$ from a convex mirror of focal length $30 \ cm$. $A$ plane mirror is now placed in such a way that the image produced by both the mirrors coincide with each other. The distance between the two mirrors is (in $cm$)

$A$ point source $S$ is placed at a distance of $15 \; cm$ from a converging lens of focal length $10 \; cm$. Where should a concave mirror of focal length $12 \; cm$ be placed so that a real image is formed on the object itself (in $; cm$)?

How can we change a camera from $F/4$ to $F/5.6$?