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 (in $m$) of the lens required for the purpose?

$A$ 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 ...... $cm$.

An illuminated object and a screen are placed $90 \, cm$ apart. What is the focal length of the lens required to produce an image on the screen,twice the size of the object?.......$cm$

$A$ plano-convex thin lens is used to obtain the image of a point object $O$ on the screen $S$ as shown in the figure. The thickness of the lens in the middle is $0.5 \ cm$ and the refractive index of the material of the lens is $1.5$. If the separation $D$ between the object and the screen is to be minimum,then the aperture diameter of the lens should be.....$cm$.

$A$ lens of refractive index $n$ is placed in a liquid of refractive index $n'$. If the focal length of the lens in air is $f$,what will be its focal length in the liquid?

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