$A$ double convex lens has a focal length of $25\; cm$. The radius of curvature of one of the surfaces is double the other. Find the radii if the refractive index of the material of the lens is $1.5$.

$A$ hollow double concave lens is made of very thin transparent material. It can be filled with air or either of two liquids $L_1$ and $L_2$ having refractive indices $n_1$ and $n_2$ respectively $(n_2 > n_1 > 1)$. The lens will diverge a parallel beam of light if it is filled with

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 $\,cm$)

For a convex lens,if a real image is formed,the graph between $(u + v)$ and $u$ or $v$ is as follows:

Write the lens maker's equation for a thin lens.

In the diagram shown,the lens is moving towards the object with a velocity $V \, m/s$ and the object is also moving towards the lens with the same speed. What is the speed of the image with respect to the earth when the object is at a distance $2f$ from the lens? ($f$ is the focal length.)