The radius of curvature of the curved face of a plano-convex lens is $12 \,cm$ and its refractive index is $1.5$. Then,the focal length of the lens is (in $\,cm$)

$A$ convex lens of refractive index $1.5$ and focal length $18 \, cm$ in air is immersed in water. The change in focal length of the lens will be $........... \, cm$. (Given refractive index of water $= 4/3$)

Write the Gaussian equation for a lens.

An object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.

The distance $v$ of the real image formed by a convex lens is measured for various object distances $u$. $A$ graph is plotted between $v$ and $u$. Which one of the following graphs is correct?

$A$ 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 $, cm$)?