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?

A $10 \mathrm{cm}$ long pin lies along the principal axis of a convex lens of focal length $10 \mathrm{cm}$ such that the nearer end of the pin is at a distance of $15 \mathrm{cm}$ from the lens. Find the length of the image of the pin formed by the lens.

A thin convex lens forms the distinct image of an object on a screen placed at a distance of $30 \mathrm{cm}$ from the lens. When the lens is displaced $5 \mathrm{cm}$ towards the screen, then in order to obtain distinct image the screen is displaced $5 \mathrm{cm}$ towards the lens. Find the focal length of the lens.

An object is placed infront a convex lens at such a distance that its real image of the same size is formed. When the object is displaced $16 \mathrm{cm}$ towards the lens, still a real image is formed but now its size is 3 times the size of the object. Calculate the focal length of the lens.