An object is placed $50\, cm$ from a lens that produces a virtual image at a distance of $10\, cm$ in front of the lens. Calculate the focal length of the lens. (in $, cm$)

An object of height $5 \, cm$ is placed perpendicular to the principal axis of a concave lens of focal length $10 \, cm$. If the distance of the object from the optical centre of the lens is $20 \, cm$,determine the position,nature,and size of the image formed using the lens formula.

What is the power of a convex lens with a focal length of $20 \text{ cm}$?

With the help of a ray diagram,show the formation of an image by a convex lens when the object is placed between $F$ and $2F$. Write two characteristics of the image so formed.

Where should an object be placed so that a real and inverted image of the same size is obtained by a convex lens?

What type of lens behaviour will an air bubble inside water show?