The power of a biconvex lens is $1.25\,m^{-1}$ in a particular medium. The refractive index of the lens is $1.5$ and the radii of curvature are $20\,cm$ and $40\,cm$ respectively. Find the refractive index of the surrounding medium.

$A$ 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 $(\mu_{w}=\frac{4}{3})$?

An object is placed at a distance of $20 \ cm$ from a convex lens of focal length $10 \ cm$. The image is formed on the other side of the lens at a distance of . . . . . . $cm$.

The distance between an object and its two times magnified real image produced by a convex lens is $45 \,cm$. The focal length of the lens used is . . . . . . $cm$.

$A$ turnip sits before a thin converging lens,outside the focal point of the lens. The lens is filled with a transparent gel so that it is flexible; by squeezing its ends toward its center [as indicated in figure $(a)$],you can change the curvature of its front and rear sides. What happens to the lateral height of the image?

$A$ lens is placed between a source of light and a wall. It forms images of area $A_1$ and $A_2$ on the wall for its two different positions. The area of the source of light is