The distance between an object and its $3$ times magnified virtual image produced by a convex lens is $20 \,cm$. The focal length of the lens used is: (in $\,cm$)

$A$ parallel beam of light is incident on a converging lens parallel to its principal axis. As one moves away from the lens on the other side along the principal axis,the intensity of light

The power of a thin convex lens placed in air is $+4 \ D$. The refractive index of the material of the convex lens is $\frac{3}{2}$. If this convex lens is immersed in a liquid of refractive index $\frac{5}{3}$, then

Letters $A, B, C$ and $D$ are written on a cardboard as shown in the figure. The cardboard is kept at a suitable distance behind a transparent empty glass of cylindrical shape. If the glass is now filled with water,one sees an inverted image of the pattern on the cardboard when looking through the glass. Ignoring magnification effects,the image would appear as:

$A$ double convex lens,made of a material of refractive index $\mu_1$,is placed inside two liquids of refractive indices $\mu_2$ and $\mu_3$ as shown,where $\mu_2 > \mu_1 > \mu_3$. $A$ wide,parallel beam of light is incident on the lens from the left. The lens will give rise to:

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I$. If the central region of the lens with aperture diameter $\frac{d}{2}$ is covered by black paper,what will be the new focal length and intensity of the image?