$A$ double convex lens is made of glass of refractive index $1.5$. If its focal length is $30 \ cm$,then the radius of curvature of each of its curved surfaces is:

An achromatic combination is made with a lens of focal length $f$ and dispersive power $\omega$ with a lens having a dispersive power of $2\omega$. The focal length of the second lens will be:

$A$ bulb is located on a wall. Its image of equal size is to be obtained on a parallel wall with the help of a convex lens. The lens is placed at a distance $d$ ahead of the second wall. The required focal length will be:

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?

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

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 $cm$)