An object has an image thrice of its original size when kept at $8 \ cm$ and $16 \ cm$ from a convex lens. The focal length of the lens is:

Define power of a lens,obtain its equation and write its $SI$ unit.

An equiconvex lens of radius of curvature $14 \ cm$ is made up of two different materials. The left half and right half of the vertical portion are made up of materials with refractive indices $1.5$ and $1.2$ respectively,as shown in the figure. If a point object is placed at a distance of $40 \ cm$,calculate the image distance. (in $cm$)

$A$ magnifying lens has a focal length of $10 \, cm$. If the image is formed at a distance of $30 \, cm$ from the lens,what is the magnification?

An object is placed at a certain distance to the left of a convex lens of focal length $20 \,cm$. Find the distance of the object if the image obtained is magnified by $4$ times.

Write the Gaussian equation for a lens.