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?

Inside a vessel filled with liquid, a converging lens is placed as shown in the figure. The lens has a focal length of $15 \,cm$ when in air and has a refractive index of $\frac{3}{2}$. If the liquid has a refractive index of $\frac{9}{5}$, the focal length of the lens in the liquid is (in $\,cm$)

$A$ plano-concave lens is made of glass of refractive index $1.5$ and the radius of curvature of its curved face is $100 \,cm$. What is the power of the lens?

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?

If a lens is moved towards the object from a distance of $40 \,cm$ to $30 \,cm$,the magnification of the image remains the same (numerically). The focal length of the lens is ......... $cm$.

$A$ double convex lens has a focal length of $25\; cm$. The radius of curvature of one of the surfaces is double the other. Find the radii if the refractive index of the material of the lens is $1.5$.