$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a convex lens of focal length $20 \, cm$ (in $, cm$)?

$A$ double convex thin lens made of glass (refractive index $\mu = 1.5$) has both radii of curvature of magnitude $20 \ cm$. Incident light rays parallel to the axis of the lens will converge at a distance $L$ such that $L = ...... \ cm$.

The power of an equi-concave lens is $-4.5 \ D$ and it is made of a material with a refractive index of $1.6$. The radius of curvature of the lens is: (in $cm$)

In the case of the displacement method of lenses,the product of magnification in both cases is

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 object is placed at a distance of $5 \, cm$ from the first principal focus of a convex lens of focal length $10 \, cm$. If a real image is formed,find its distance from the lens in $cm$.