The plane faces of two identical plano-convex lenses,each with focal length $f$,are pressed against each other using an optical glue to form a convex lens. The distance from the optical centre at which an object must be placed to obtain an image of the same size as the object is

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both curved surfaces have the same radius of curvature $R = 14\, cm$. For this bi-convex lens,for an object distance of $40\, cm$,the image distance will be.....$ cm$

Two thin lenses,one of focal length $+ 60 \ cm$ and the other of focal length $-20 \ cm$ are put in contact. The combined focal length is........$cm$.

$A$ bi-convex lens is formed with two thin plano-convex lenses as shown in the figure. The refractive index $n$ of the first lens is $1.5$ and that of the second lens is $1.2$. Both the curved surfaces are of the same radius of curvature $R = 14 \, cm$. For this bi-convex lens,for an object distance of $40 \, cm$,the image distance will be.......$cm$

The focal length (in $cm$) of a lens with dispersive power $0.45$ that should be placed in contact with a convex lens of focal length $84 \,cm$ and dispersive power $0.21$ to form an achromatic combination is:

$A$ glass convex lens of focal length $0.1 \ m$ is cut into two equal parts along its axis. The ratio of the focal length of the new lenses is: