In order to obtain a real image of magnification $2$ using a converging lens of focal length $20 \ cm,$ where should an object be placed in $cm$?

An object is placed at a distance $x$ from the focus of a convex lens,and its image is formed at a distance $x'$ from the other focus,as shown in the figure. Which relation do the distances $x$ and $x'$ satisfy?

If in a plano-convex lens,the radius of curvature of the convex surface is $10 \,cm$ and the focal length of the lens is $30 \,cm$,the refractive index of the material of the lens will be ..........

$A$ convex lens of focal length $1/3 \ m$ forms a real,inverted image twice the size of the object. The distance of the object from the lens is: (in $m$)

Focal length of a convex lens will be maximum for

$(i)$ 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 $= 1.5$)