Two lenses of power $-15 \ D$ and $+5 \ D$ are in contact with each other. The focal length of the combination is ....... $cm$.

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:

In the figure shown here,what is the equivalent focal length (in $cm$) of the combination of lenses (Assume that all layers are thin)?

$A$ combination of two thin lenses with focal lengths $f_1$ and $f_2$ respectively forms an image of a distant object at a distance of $60 \ cm$ when the lenses are in contact. The position of this image shifts by $30 \ cm$ towards the combination when the two lenses are separated by $10 \ cm$. The corresponding values of $f_1$ and $f_2$ are:

As shown in the figure, a combination of a thin plano-concave lens and a thin plano-convex lens is used to image an object placed at infinity. The radius of curvature of both the lenses is $30\,cm$ and the refractive index of the material for both the lenses is $1.75$. Both the lenses are placed at a distance of $40\,cm$ from each other. Due to the combination, the image of the object is formed at a distance $x = ..........cm$ from the concave lens.

$A$ convex lens of focal length $40 \, cm$ and a concave lens of focal length $25 \, cm$ are placed in contact. The power of the combination is .......... $D$.