The focal length of a thin biconvex lens is $20 \,cm$. When an object is moved from a distance of $25 \,cm$ in front of it to $50 \,cm$, the magnification of its image changes from $m_{25}$ to $m_{50}$. The ratio $\frac{m_{25}}{m_{50}}$ is

An object placed $10 \ cm$ in front of a lens has an image $20 \ cm$ behind the lens. What is the power of the lens (in dioptres)?

$A$ thin convex lens made from crown glass $\left( \mu = \frac{3}{2} \right)$ has focal length $f$. When it is measured in two different liquids having refractive indices $\frac{4}{3}$ and $\frac{5}{3}$,it has the focal lengths $f_1$ and $f_2$ respectively. The correct relation between the focal lengths is:

$A$ convex lens has a focal length of $0.3 \ m$ and a refractive index of $3/2$. Find the focal length of the lens in $m$ when it is immersed in water,which has a refractive index of $4/3$.

$A$ card sheet divided into squares each of size $1 \, mm^2$ is being viewed at a distance of $9 \, cm$ through a magnifying glass (a converging lens of focal length $10 \, cm$) held close to the eye. What is the magnification produced by the lens?

The refractive index of the material of a double convex lens is $1.5$ and its focal length is $5 \,cm$. If the radii of curvature are equal, the value of the radius of curvature (in $cm$) is