Inside a vessel filled with liquid, a converging lens is placed as shown in the figure. The lens has a focal length of $15 \,cm$ when in air and has a refractive index of $\frac{3}{2}$. If the liquid has a refractive index of $\frac{9}{5}$, the focal length of the lens in the liquid is (in $\,cm$)

An extended object is placed at point $O$,$10 \ cm$ in front of a convex lens $L_1$ and a concave lens $L_2$ is placed $10 \ cm$ behind it,as shown in the figure. The radii of curvature of all the curved surfaces in both the lenses are $20 \ cm$. The refractive index of both the lenses is $1.5$. The total magnification of this lens system is

$A$ convex lens of focal length $20 \ cm$ produces images of the same magnification $2$ when an object is kept at two distances $x_1$ and $x_2$ $(x_1 > x_2)$ from the lens. The ratio of $x_1$ and $x_2$ is

$A$ lens with a focal length of $50 \ cm$ forms an image of a distant object that subtends an angle of $1 \text{ milliradian}$ at the lens. What is the size of the image in $mm$?

$f_V$ and $f_R$ are the focal lengths of a convex lens for violet and red light respectively,and $F_V$ and $F_R$ are the focal lengths of a concave lens for violet and red light respectively. Then:

An object is placed at the focus of a concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?