The refractive index of a converging lens is $1.4$. What will be the focal length of this lens if it is placed in a medium of the same refractive index? (Assume the radii of curvature of the faces of the lens are $R_{1}$ and $R_{2}$ respectively)

Let $u$ and $v$ be the distances of the object and the image from a lens of focal length $f$. The correct graphical representation of $u$ and $v$ for a convex lens when $|u|>f$,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-concave lens and second image from the planar 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?

The sun subtends an angle of $(1/2)^o$ at the surface of the earth. $A$ converging lens of focal length $100\, cm$ is used to obtain an image of the sun on a screen. The diameter of the image formed is about.....$mm$.

$A$ double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power $1.5P$ is ......$R$.

The ratio of the focal lengths of a convex lens when kept in air and when it is immersed in a liquid is $1: 2$. If the refractive index of the material of the lens is $1.5$,then the refractive index of the liquid is