The size of the images of an object, formed by a thin lens, are equal when the object is placed at two different positions $8 \ cm$ and $24 \ cm$ from the lens. The focal length of the lens is . . . . . . $cm$.

In the displacement method,the distance between the object and the screen is $70 \; cm$ and the focal length of the lens is $16 \; cm$. Find the separation between the magnified and diminished image positions of the lens. (in $; cm$)

$A$ thin equiconvex lens is made of glass of refractive index $1.5$ and its focal length is $0.2 \ m$. If it acts as a concave lens of $0.5 \ m$ focal length when dipped in a liquid,the refractive index of the liquid is:

$A$ point source of light is moving at a rate of $2 \,cm \,s^{-1}$ towards a thin convex lens of focal length $10 \,cm$ along its optical axis. When the source is $15 \,cm$ away from the lens,the image is moving at:

The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit $S$ and the collimating lens $L$ is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure:

$A$ plano-convex lens is made of material having refractive index $1.5$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is . . . . . . $cm$.