Spherical Lens Instead of Parabolic Lens I know that using the paraxial approximation, spherical lenses behave like parabolic lenses.
It seems that there is no reason to use spherical lenses instead of parabolic (because they are used in the same way, and parabolic lenses do not required paraxial approximation) apart from the fact that parabolic lenses are more complicated to make.

*

*Does spherical lenses have more advantages over parabolic lenses?

*Are there any application that required specifically spherical lenses (and not parabolic)?

 A: Spherical reflectors have the outstanding advantage over parabolic reflectors in that by moving the feedpoint/receiver off-center above the spherical surface, the beam aperture can be steered without having to steer the entire antenna. This principle was used in the design of the radio telescope at Arecibo, PR which recently fell down when several of the cables supporting the steerable feedhorn assembly broke.
Note that because the reflections from a spherical mirror do not come to a single focus, an array of aspheric reflectors in front of the feedhorn is required to correct for this- which the Arecibo system possessed.
A: Once you deal with practical lens systems that operate at higher numerical apertures, for example a microscope objective, the paraxial conditions no longer hold. Spherical surface can be made highly accurately, and then combined in order to control aberrations precisely in a way that would be much more expensive with any other type of surface.
Spherical surfaces are the natural outcome of polishing two materials against each other, so people have been making spherical surfaces for hundreds of years. There is an entire industry built up around the generation and mounting of spherical surfaces. That is why they are significantly cheaper than aspheric surfaces and usually of higher quality.  (In some cases, the design objectives for a lens can not be achieved with spherical surfaces, and then aspheres will offer an advantage).
