$A$ thin double convex lens has radii of curvature each of magnitude $40 \; cm$ and is made of glass with refractive index $1.65$. Its focal length is nearly....... $cm$.

The thickness at the centre of a plano-convex lens is $3 \, mm$ and the diameter is $6 \, cm$. If the speed of light in the material of the lens is $2 \times 10^{8} \, m/s$,the focal length of the lens is ............ $cm$.

In the displacement method,the distance between the object and the screen is $70 \; cm$ and the focal length of the lens is $16 \; cm$. Find the separation between the magnified and diminished image positions of the lens. (in $; cm$)

At what distance from a convex lens of focal length $30 \ cm$, an object should be placed so that the size of the image is $1/2$ of the object (in $cm$)?

What is the relative decrease in focal length of a lens for an increase in optical power by $0.1 \ D$ from $2.5 \ D$? [$D$ stands for dioptre]

$A$ convex lens is used to form an image of an object on a screen. If the upper half of the lens is blackened,so that it becomes opaque,then