A lens is a transparent refracting medium bounded by two spherical surfaces.R1 and R2 are radii of two surfaces.

Will the Radii R1 and R2 will be same or different ?

I hope that they are same, otherwise there wont be symmetry. Still doubts lingers. Revered members can help.

 

http://scientificsentence.net/Optics/index.php?key=yes&Integer=lenses

 

The radii may be the same or they may be different.

A common variant of lens used in telescope eyepieces has one flat surface and one curved surface.

There is no need for opposite sides of a lens to be symmetrical.

 

It depends upon the use of the lens. There are several ways to remedy the faults of lenses viz. aberration, astigmatism, chromatic aberration etc, which may be corrected by designing several lenses one after another, and having a combination of spehrical and plano surfaces.