The focal length of a convex lens is $30 \ cm$ and the size of the image is a quarter of the object,then the object distance is ........ $cm$.

$A$ square card of side length $1\, mm$ is being seen through a magnifying lens of focal length $10\, cm$. The card is placed at a distance of $9\, cm$ from the lens. The axis is perpendicular to the plane of the card. The apparent area of the card through the lens is......$cm^2$

An equiconvex lens made of glass of refractive index $\frac{3}{2}$ has focal length $f$ in air. It is completely immersed in water of refractive index $\frac{4}{3}$. The percentage change in the focal length is

When a plane wavefront is incident on a convex lens,the emerging wavefront becomes . . . . . . .

An object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.

If the radii of curvature of both convex surfaces of a lens are $20 \, cm$,find the focal length of the lens in the given arrangement. (in $, cm$)