$A$ magnifying glass is to be used at a fixed object distance of $1 \text{ inch}$. If it is to produce an erect image magnified $5$ times,its focal length should be ........ $\text{inch}$.

$A$ lens is made of flint glass (refractive index $= 1.5$). When the lens is immersed in a liquid of refractive index $1.25$,the focal length

In the displacement method,a convex lens is placed between an object and a screen. If the magnifications in the two positions are $m_1$ and $m_2$ and the displacement of the lens between the two positions is $x$,then the focal length of the lens is:

$A$ magnifying lens has a focal length of $10 \, cm$. If the image is formed at a distance of $30 \, cm$ from the lens,what is the magnification?

An object is placed at a distance of $20 \ cm$ from a convex lens of focal length $10 \ cm$. The image is formed on the other side of the lens at a distance of . . . . . . $cm$.

$A$ thin converging lens of focal length $f=25 \,cm$ forms the image of an object on a screen placed at a distance of $75 \,cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object has to be shifted, so that its image on the screen is sharp again, is (in $\,cm$)