The radii of curvature of a double convex lens are $4 \ cm$ and $8 \ cm$. If the refractive index of the material of the lens is $1.5$,the focal length of the lens is nearly (in $cm$)

Write the lens formula for a thin lens.

The radii of curvature of the faces of a double convex lens are $10\,cm$ and $15\,cm$. Its focal length is $12\,cm$. What is the refractive index of glass?

An object is placed at a distance of $4\,cm$ in front of a concave lens of focal length $12\,cm$. The nature and position of the image from the lens is

$A$ lens forms real and virtual images of an object when the object is at $u_1$ and $u_2$ distances respectively. If the size of the virtual image is double that of the real image,then the focal length of the lens is (Take the magnification of the real image as $m$)

$A$ point object is placed $20 \,cm$ to the left of a convex lens of focal length $f=5 \,cm$. The lens is made to oscillate with a small amplitude $A$ along the horizontal axis. The image of the object will also oscillate along the axis with: