What can you tell about the image of a $3 \mathrm{cm}$ long object placed at a distance of $15 \mathrm{cm}$ from a lens, if the magnification is known to be $-2$?

The diameter of the sun is$1.4\times {10}^9\mathrm{m}$ . Find the diameter of the image of the sun formed by a convex lens of focal length $1.0 \mathrm{m}$. The distance of the sun from the earth is $\begin{array}{l}1.0\times {10}^{11}\mathrm{m}\end{array}$.

A double concave lens of glass $(n = 1.5)$ has both radii of curvature of magnitude $40 \mathrm{cm}$. An object $2 \mathrm{cm}$ high is placed at $10 \mathrm{cm}$ from the lens. Find the position, size and nature of the image.

A lens of focal length $12 \mathrm{cm}$ produces a virtual image of size $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.$ that of the object. Find the nature of the lens and the positions of the object and the image.

A convex lens of focal length $12 \mathrm{cm}$ produces an image on a screen three times in size than the object. What is the distance of the object from the lens?

A convex lens forms 19 times magnified image of an object on a screen placed $10 \mathrm{m}$ from the lens. What is the focal length of the lens?