Math Optics is a mathematical theory of imaging, of which there are several. Optics most accurate theory of imaging that includes wavelength dependent phenomena, such as interference and diffraction . Optics ray theory of imaging that ignores interference and diffraction.
Geometric optics is the short wavelength limit of physical optics.
The essential characteristic of geometric optics is that light propagates along straight lines or rays through homogeneous media. When a refractive index difference is encountered, ray refraction is exactly described by Snell's law . The paraxial approximation is physically valid only when all rays make vanishing small angles to the prerequisite but arbitrary power axis . A paraxial model does not include the surface shape information responsible for inducing optical aberration. To evaluate aberration, a more exact theory of imaging must be used.