$A$ substance is behaving as a convex lens in air and a concave lens in water. What is its refractive index?

What is the focal length (in $cm$) of a biconvex lens with a radius of curvature of $40\, cm$ and a refractive index of $1.65$?

The graph between $\frac{1}{u}$ and $\frac{1}{v}$ for a thin convex lens in order to determine its focal length is plotted as shown in the figure. The refractive index of the lens is $1.5$ and both its surfaces have the same radius of curvature $R$. The value of $R$ will be in $cm$.
(Where $u =$ object distance,$v =$ image distance)

The focal length of a thin biconvex lens is $20 \,cm$. When an object is moved from a distance of $25 \,cm$ in front of it to $50 \,cm$, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is

The graph shows how the magnification $m$ produced by a convex thin lens varies with image distance $v$. What was the focal length of the used lens?

The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)