$A$ point object in air is in front of the curved surface of a plano-convex lens. The radius of curvature of the curved surface is $30 \; cm$ and the refractive index of the lens material is $1.5$. Then the focal length of the lens (in $cm$) is:

$(i)$ If $f=0.5 \,m$ for a glass lens,what is the power of the lens?
$(ii)$ The radii of curvature of the faces of a double convex lens are $10 \,cm$ and $15 \,cm$. Its focal length is $12 \,cm$. What is the refractive index of glass?
$(iii)$ $A$ convex lens has $20 \,cm$ focal length in air. What is its focal length in water? (Refractive index of water $= 1.33$,refractive index of glass $= 1.5$)

The optical axis of a thin equiconvex lens is the $x$-axis. The coordinates of the object and its image are $(-40 \, cm, 1 \, cm)$ and $(50 \, cm, -2 \, cm)$ respectively. Find the position of the lens.

$A$ plano-convex lens is made of refractive index $1.6$. The radius of curvature of the curved surface is $60 \ cm$. The focal length of the lens is $..... \ cm$.

$A$ concave lens of focal length $f$ produces an image $(1/x)$ of the size of the object. The distance of the object from the lens is:

Double-convex lenses are to be manufactured from a glass of refractive index $1.55$,with both faces of the same radius of curvature. What is the radius of curvature (in $cm$) required if the focal length is to be $20\;cm$?