The image of a small electric bulb fixed on the wall of a room is to be obtained on the opposite wall $3\, m$ away by means of a large convex lens. What is the maximum possible focal length of the lens required for the purpose?

At what distance from a convex lens of focal length $30 \ cm$, an object should be placed so that the size of the image is $1/2$ of the object (in $cm$)?

$A$ thin lens of material having refractive index $\mu = 1.5$ and focal length of $20 \ cm$ in air has two media of different refractive indices $\mu_1 = 1.2$ and $\mu_2 = 2.5$ covering the upper and lower halves of the lens,respectively,as shown in the figure. If an object is placed on the principal axis,then its two images will be formed,one after refraction from the upper part and the other after refraction from the lower part. Considering the object to be at $\infty$,the separation between the two images formed would be ...... $cm$.

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?

$A$ convex lens of focal length $\frac{1}{3} \ m$ forms a real,inverted image twice the size of the object. The distance of the object from the lens is (in $m$)

The distance between an object and the screen is $100 \ cm$. $A$ lens produces an image on the screen when placed at either of the positions $40 \ cm$ apart. The power of the lens is