The dispersive powers of the glasses of lenses used in an achromatic pair are in the ratio $5 : 3$. If the focal length of the concave lens is $15 \ cm$,then the nature and focal length of the other lens would be:

$A$ double convex lens is made of glass of refractive index $1.5$. If its focal length is $30 \ cm$,then the radius of curvature of each of its curved surfaces is:

For a given lens,the magnification was found to be twice as large when the object was $0.15 \ m$ distant from it as when the distance was $0.2 \ m$. The focal length of the lens is.......$m$.

The figure given below shows a beam of light converging at point $P.$ When a concave lens of focal length $16 \ cm$ is introduced in the path of the beam at a place $O$ shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to.....$cm$.

Define power of a lens and write the $SI$ unit of power.

In an experiment to measure the focal length $(f)$ of a convex lens,the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y-x$ plot is shown in the figure. The focal length of the lens is . . . . . . $cm$.