$f_V$ and $f_R$ are the focal lengths of a convex lens for violet and red light respectively,and $F_V$ and $F_R$ are the focal lengths of a concave lens for violet and red light respectively. Then:

An object is placed at a distance of $1.50 \, m$ from a screen. $A$ convex lens is placed between them to form a real image four times larger than the object on the screen. The position of the lens is at a distance of ..... (in $, m$)

The figure given below shows a beam of light converging at point $P.$ When a concave lens of focal length $16 \ cm$ is introduced in the path of the beam at a place $O$ shown by the dotted line such that $OP$ becomes the axis of the lens,the beam converges at a distance $x$ from the lens. The value of $x$ will be equal to.....$cm$.

An equiconvex lens is cut into two halves along $(i) XOX'$ and $(ii) YOY'$ as shown in the figure. Let $f, f', f''$ be the focal lengths of the complete lens,of each half in case $(i),$ and of each half in case $(ii),$ respectively. Choose the correct statement from the following:

The radius of curvature of a convex lens is $40 \,cm$ for each surface. Its refractive index is $1.5$. Its focal length is: (in $\,cm$)

The diameter of a plano-convex lens is $6 \, cm$ and its thickness at the centre is $3 \, mm$. If the speed of light in the material of the lens is $2 \times 10^8 \, m/s$,the focal length of the lens is.......$cm$.