The minimum distance between an object and its real image formed by a convex lens is

If in a plano-convex lens,the radius of curvature of the convex surface is $10 \,cm$ and the focal length of the lens is $30 \,cm$,the refractive index of the material of the lens will be ..........

Two transparent media of refractive indices $\mu_1$ and $\mu_3$ have a solid lens-shaped transparent material of refractive index $\mu_2$ between them as shown in the figures in Column $II$. $A$ ray traversing these media is also shown in the figures. In Column $I$,different relationships between $\mu_1, \mu_2$,and $\mu_3$ are given. Match them to the ray diagram shown in Column $II$.

$A$ photograph of a landscape is captured by a drone camera at a height of $18 \ \text{km}$. The size of the camera film is $2 \ \text{cm} \times 2 \ \text{cm}$ and the area of the landscape photographed is $400 \ \text{km}^2$. The focal length of the lens in the drone camera is: (in $\text{cm}$)

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

$A$ thin equiconvex lens is made of glass of refractive index $1.5$ and its focal length is $0.2 \ m$. If it acts as a concave lens of $0.5 \ m$ focal length when dipped in a liquid,the refractive index of the liquid is: