Lens Formula and Magnification Formulae for a Concave Lens

A concave lens produces an image $20 \mathrm{cm}$ from the lens of an object placed $30 \mathrm{cm}$ from the lens. The focal length of the lens is:

The diverging lens of focal length $100 \mathrm{mm}$ is replaced by a converging lens also of focal length $100 \mathrm{mm}$. The object is placed $150 \mathrm{mm}$ away from the lens and an image is formed by the converging lens. Compare two properties of this image with those of the image formed by the diverging lens.

A small object is placed $150 \mathrm{mm}$ away from a diverging lens of focal length $100 \mathrm{mm}$.

Calculate the distance of the image from the lens by using the lens formula.

Find the position and size of the virtual image formed when an object $2 \mathrm{cm}$ tall is placed $20 \mathrm{cm}$ from: A diverging lens of focal length $40 \mathrm{cm}$.

A $2.0 \mathrm{cm}$ tall object is placed $40 \mathrm{cm}$ from a diverging lens of focal length $15 \mathrm{cm}$. Find the position and size of the image.

A concave lens has a focal length of $20 \mathrm{cm}$. At what distance from the lens a $5 \mathrm{cm}$ tall object be placed so that it forms an image at $15 \mathrm{cm}$ from the lens? Also calculate the size of the image formed.

Calculate the image distance for an object of height $12 \mathrm{mm}$ at a distance of $0.20 \mathrm{m}$ from a concave lens of focal length $0.30 \mathrm{m}$, and state the nature and size of the image.

A concave lens has focal length $15 \mathrm{cm}$. At what distance should the object from the lens be placed so that it forms an image at $10 \mathrm{cm}$ from the lens? Also find the magnification produced by the lens.

A concave lens of $20 \mathrm{cm}$ focal length forms an image $15 \mathrm{cm}$ from the lens. Compute the object distance.

A concave lens of focal length $15 \mathrm{cm}$ forms an image $10 \mathrm{cm}$ from the lens. How far is the object placed from the lens? Draw the ray-diagram.

An object is placed at a distance of $4 \mathrm{cm}$ from a concave lens of focal length $12 \mathrm{cm}$. Find the position and nature of the image.

The lens $A$ produces a magnification of, $-0.6$ whereas lens $B$ produces a magnification of $+0.6$.

What is the nature of lens $B$? 

(Choose from: Convex / Concave / Plano-Convex)

How could you find the focal length of a convex lens rapidly but approximately?