The focal length of a plano-convex lens is equal to its radius of curvature. Find the refractive index of its material.

$A$ convex lens of refractive index $1.5$ has power $3D$. It is placed in a liquid of refractive index $2$. The new power of the lens is (in $D$)

$A$ point object is moving at a constant speed of $1 \,ms^{-1}$ along the principal axis of a convex lens of focal length $10 \,cm$. The speed of the image is also $1 \,ms^{-1}$, when the object is at what distance (in $cm$) from the optical centre of the lens?

$A$ lens of focal power $0.5 D$ is

An object is placed at the focus of a concave lens having focal length $f$. What is the magnification and distance of the image from the optical centre of the lens?

$f_v$ and $f_r$ are the focal lengths of a convex lens for violet and red lights respectively,and $F_v$ and $F_r$ are the magnitudes of the focal lengths of a concave lens for violet and red lights respectively. Then: