$A$ convex lens $T$ is used to form an image whose size is one-fourth that of the size of the object. Then the object distance is (in $f$)

$A$ convex 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........$cm$.

The focal length of a thin converging lens in air is $20 \ cm$. When the lens is immersed in a liquid,it behaves like a concave lens of power $1 \ D$. If the refractive index of the material of the lens is $1.5$,the refractive index of the liquid is

$A$ convex lens forms a real image of an object for its two different positions on a screen. If the height of the image in both cases is $8 \ cm$ and $2 \ cm$,then the height of the object is ........ $cm$.

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 glass?