An object is placed at $15 \, cm$ from a convex lens of focal length $20 \, cm$. Which of the following is correct?

The relation between $n_1$ and $n_2$,if the behavior of light rays is as shown in the figure,is:

$A$ bi-concave glass lens having refractive index $1.5$ has both surfaces of same radius of curvature $R$. On immersion in a medium of refractive index $1.75$,it will behave as a

The dotted part of the lens is cut and kept on the $x$-axis as shown in the diagram. If parallel paraxial rays are falling on this system,then the coordinate of the image formed after refraction from both the lenses is $(30, -1)$. If $x = 2.5 \, cm$,then $y = .......... \, cm$. (Assume the lens has no spherical aberration)

Consider the following statements regarding the real images formed with a converging lens.
$I$. Real images can be seen only if the image is projected onto the screen.
$II$. The real image can be seen only from the same side of the lens as that on which the object is positioned.
$III$. Real images produced by converging lenses are not only laterally but also longitudinally inverted as with mirrors.
Which of the above statement$(s)$ is/are incorrect?

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 $\,cm$)