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]

$A$ biconvex lens of radius of curvature $R$ is made up of a variable refractive index $\mu = 2[1 + \frac{|y|}{d}]$. Assume $2d << R$. $A$ point object is placed at a distance $R$ on the principal axis as shown in the figure. If the spread of the image lies over a span of $n$ meters,find the value of $n$.

The graph shows how the magnification $m$ produced by a convex thin lens varies with image distance $v$. What was the focal length of the used lens?

If in a plano-convex lens,the radius of curvature of the convex surface is $10 \ cm$ and the focal length of the lens is $30 \ cm,$ then the refractive index of the material of the lens will be

$A$ screen is placed $100 \,cm$ from an object. The image of the object on the screen is formed by a convex lens at two different locations separated by $20 \,cm$. The focal length of the lens is (in $\,cm$)

The refractive index of a glass convex lens is $1.5$. The radius of curvature of each of the two surfaces of the lens is $40 \ cm$. The ratio of the power of the lens when immersed in a liquid of refractive index $1.25$ to that when placed in air is: