The focal length of a lens is $10 \ cm$. What is the power of the lens in dioptre (in $D$)?

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........$cm$.

$A$ lens is placed between a source of light and a wall. It forms images of area $A_1$ and $A_2$ on the wall for its two different positions. The area of the source of light is

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I.$ If an aperture of diameter $\frac{d}{2}$ in the central region of the lens is covered by a black paper,the focal length of the lens and the intensity of the image will be,respectively:

$A$ glass concave lens is placed in a liquid in which it behaves like a convergent lens. If the refractive indices of glass and liquid with respect to air are $^a{\mu _g}$ and $^a{\mu _l}$ respectively,then

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 the material of the lens?