$A$ convex lens is dipped in a liquid whose refractive index is equal to the refractive index of the lens. Then its focal length will

$A$ thin convex lens is placed just above an empty vessel of depth $80 \,cm$. The image of a coin kept at the bottom of the vessel is thus formed $20 \,cm$ above the lens. If now water is poured in the vessel up to a height of $64 \,cm$, what will be the approximate new position of the image? Assume that the refractive index of water is $4/3$.

Write the Gaussian equation for a lens.

The image of an illuminated square is obtained on a screen with the help of a converging lens. The distance of the square from the lens is $40\,cm$. The area of the image is $9$ times that of the square. The focal length of the lens is........$cm$.

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 radii of curvature of the faces of a double convex lens are $10 \ cm$ and $15 \ cm$. Its focal length is $12 \ cm$. What is the refractive index of the material of the lens?