$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

$A$ glass convex lens $(\mu_{g}=1.5)$ has a focal length of $8 \ cm$ when placed in air. What would be the focal length of the lens in $cm$ when it is immersed in water $(\mu_{w}=\frac{4}{3})$?

$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed are

$A$ convex lens is used to form a real image of an object on a screen. It is observed that even when the positions of the object and the screen are fixed,there are two positions of the lens that form real images. If the heights of the images are $4 \ cm$ and $9 \ cm$ respectively,the height of the object is.....$cm$.

The focal length of a convex lens is maximum for which of the following?

$A$ thin lens of refractive index $1.5$ has an optical power of $-5 \ D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ is $D$.