Define power of a lens and write the $SI$ unit of power.

$A$ convex lens of refractive index $1.5$ has power $3D$. It is placed in a liquid of refractive index $2$. The new power of the lens is (in $D$)

For a concave lens of focal length $f$,the relation between object distance $u$ and image distance $v$ from its pole can best be represented by ($u = v$ is the reference line):

$A$ magnifying glass is to be used at a fixed object distance of $1 \text{ inch}$. If it is to produce an erect image magnified $5$ times,its focal length should be ........ $\text{inch}$.

Two thin lenses having $R_1$ and $R_2$ as the radii of curvature of their surfaces are kept coaxially together. Their power is proportional to

$A$ plano-convex lens having a radius of curvature of the first surface $2 \ cm$ exhibits a focal length of $f_1$ in air. Another plano-convex lens with a first surface radius of curvature $3 \ cm$ has a focal length of $f_2$ when it is immersed in a liquid of refractive index $1.2$. If both lenses are made of the same glass of refractive index $1.5$,the ratio of $f_1$ and $f_2$ will be: