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 $cm$)?

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 $, cm$)

$A$ 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 $\,cm$)

In the displacement method of a lens,we obtain two images for different positions of the lens. One image is magnified,and the other is diminished. If $m$ is the magnification of the first image,then the focal length of the lens is given by:

An object is placed at a distance $m$ times the focal length of a divergent lens. The size of the image is shorter than that of the object by what factor?

Consider an equi-convex lens of glass $\left( \mu = \frac{3}{2} \right)$. If the temperature of the lens is increased by $40\, ^\circ C$,its focal length remains the same. The coefficient of linear expansion of glass is $2.5 \times 10^{-4} / ^\circ C$. Calculate the change in the refractive index of the glass on increasing the temperature by $40\, ^\circ C$.