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 . . . . . . $cm$.

Sunlight of intensity $1.3 \text{ kW m}^{-2}$ is incident normally on a thin convex lens of focal length $20 \text{ cm}$. Ignore the energy loss of light due to the lens and assume that the lens aperture size is much smaller than its focal length. The average intensity of light,in $\text{kW m}^{-2}$,at a distance $22 \text{ cm}$ from the lens on the other side is. . . . .

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.....$cm$.

$A$ plano-convex lens is made of material having refractive index $1.5$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is . . . . . . $cm$.

$A$ convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis,the number of images formed are

$A$ double convex lens made of glass has both radii of curvature of magnitude $20 \,cm$. Incident light rays parallel to the axis of the lens will converge to a point at a distance $L$ from the common pole $P$. The value of $L$ is [Refractive index of glass $= 1.5$].