If the radii of curvature of both convex surfaces of a lens are $20 \, cm$,find the focal length of the lens in the given arrangement. (in $, cm$)

$A$ planoconvex lens has a maximum thickness of $6 \,cm$. When placed on a horizontal table with the curved surface in contact with the table surface, the apparent depth of the bottommost point of the lens is found to be $4 \,cm$. If the lens is inverted such that the plane face of the lens is in contact with the surface of the table, the apparent depth of the centre of the plane face is found to be $\left(\frac{17}{4}\right) \,cm$. The radius of curvature of the lens is (in $\,cm$)

$A$ lens having refractive index $1.6$ has a focal length of $12 \ cm$ when it is in air. Find the focal length of the lens when it is placed in water. (Take the refractive index of water as $1.28$) (in $mm$)

An object is placed in front of a convex lens,and an image of height $8 \, cm$ is formed. When the lens is moved to a new position,the image height becomes $2 \, cm$. Find the height of the object in $cm$.

$A$ concave-convex lens of refractive index $1.5$ has radii of curvature of its surfaces as $30 \ cm$ and $20 \ cm$,respectively. The concave surface is facing upwards and is filled with a liquid of refractive index $1.3$. The focal length of the liquid-glass combination will be

$A$ boy is trying to start a fire by focusing sunlight on a piece of paper using an equiconvex lens of focal length $10\, cm$. The diameter of the sun is $1.39 \times 10^9\, m$ and its mean distance from the earth is $1.5 \times 10^{11}\, m$. What is the diameter of the sun's image on the paper?