What is the refractive index of the material of a double convex lens having radii of curvature of $5 \ cm$ and $10 \ cm$ and focal length of $\frac{20}{3} \ cm$?

$A$ 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 word $KVPY$ is written on a board and viewed through different lenses such that the board is at a distance beyond the focal length of the lens. Ignoring magnification effects,consider the following statements:
$(I)$ First image has been viewed from the planar side of a plano-convex lens and second image from the convex side of a plano-convex lens.
$(II)$ First image has been viewed from the concave side of a plano-concave lens and second image from the convex side of a plano-convex lens.
$(III)$ First image has been viewed from the concave side of a plano-concave lens and second image from the planar side of a plano-convex lens.
$(IV)$ First image has been viewed from the planar side of a plano-concave lens and second image from the convex side of a plano-convex lens.
Which of the above statements are correct?

An optician prescribes a corrective lens of power $+2.0 \,D$. The focal length of the required convex lens is:

The refractive index of a material of a plano-concave lens is $5/3$, and the radius of curvature is $0.3 \,m$. The focal length of the lens in air is (in $\,m$)

The focal length of a convex lens is $f$. An object is placed at a distance $x$ from its first focal point. The ratio of the size of the real image to that of the object is