$A$ thin biconvex lens is made of glass $(\mu = 1.50)$ and both surfaces have a radius of curvature of $20 \ cm$. $A$ beam of incident light is parallel to the principal axis of the lens. The lens converges it at a distance $L \ cm$. Then $L = \dots$

Write the lens formula for a thin lens.

$A$ hollow lens is made of thin glass and in the shape of a double concave lens. It can be filled with air,water of refractive index $1.33$,or $CS_2$ of refractive index $1.6$. It will act as a diverging lens,if it is

$A$ beam of light converges at a point $P$. Now a lens is placed in the path of the convergent beam $12 \, cm$ from $P$. At what point does the beam converge if the lens is a concave lens of focal length $16 \, cm$ (in $, cm$)?

For an object placed at a distance $2.4\,m$ from a lens,a sharp focused image is observed on a screen placed at a distance $12\,cm$ from the lens. $A$ glass plate of refractive index $1.5$ and thickness $1\,cm$ is introduced between the lens and the screen such that the glass plate faces are parallel to the screen. By what distance should the object be shifted so that a sharp focused image is observed again on the screen (in $,m$)?

Provide the object distance,image distance,type,size,and magnification for an object placed in front of a thin convex lens for different positions.