An unsymmetrical double convex thin lens forms the image of a point object on its axis. Will the position of the image change if the lens is reversed?
We know that the focus of a lens is given by:
where f is the focal length of the lens, n is the refractive index of the material of the lens, and R1 and R2 are the radius of the refracting surface on the side of the object and on the other side respectively.
Let the radius of the curved surface 1 and curved surface 2 of the lens be aand brespectively.
If the object is on the side of surface 1, then following the sign conventions, we have 
and 
If the object is on the side of surface 2, then following the sign conventions, we have 
and 
The focal length remains the same in both cases.
The position of the object is given by the thin lens formula:
where f is the focal length, u is the object distance and v is the image distance. All quantities follow the Cartesian sign convention.
As f remains the same and the object distance remains the same on reversing the lens, the position of the image doesn’t change!