The focal length of a thin lens made from a material of refractive index $1.5$ is $15 \ cm$. When it is placed in a liquid of refractive index $\frac{4}{3}$,its focal length will be $..........\ cm$.

$A$ converging lens forms an image of an object on a screen. The image is real and twice the size of the object. If the positions of the screen and the object are interchanged,leaving the lens in the original position,the new image size on the screen is

The magnifications produced by a convex lens for two positions of an object are $4$ and $3$, respectively. If the distance of separation between the two positions of the object is $2 \,cm$, then the focal length of the lens is (in $\,cm$)

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)?

$A$ bi-concave glass lens having refractive index $1.5$ has both surfaces of same radius of curvature $R$. On immersion in a medium of refractive index $1.75$,it will behave as a

The radius of curvature of the convex surface of a thin plano-convex lens is $15 \ cm$ and the refractive index of its material is $1.6$. The power of the lens is