Final answer:
The maximum number of spectral lines observed is determined by quantum mechanics, whereas the practical aspect of diffraction gratings relates to the principles of electromagnetism and the electromagnetic spectrum. For small objects at high speeds or strong gravitational fields, general relativity and quantum mechanics apply respectively.
Step-by-step explanation:
The maximum number of spectral lines that can be observed in an atom's emission spectrum is determined by the energy transitions between the quantized energy levels of electrons in the atom. This is best described by quantum mechanics, which introduced the concept that energy may only be absorbed or emitted in discrete quanta. The classical theory could not explain the atomic emission spectra, leading to the development of quantum theory.
For practical applications, like determining the maximum number of lines per centimeter a diffraction grating can have to produce a maximum for the smallest wavelength of visible light, we use principles of electromagnetism. Maxwell's Equations, which predict the production of electromagnetic waves, and the electromagnetic spectrum are key to understanding these concepts.
Lastly, regarding the question about the subfield of physics suitable for describing small objects at high speeds or in strong gravitational fields, the answer is the general theory of relativity for gravitational fields and quantum mechanics for small objects at high speeds.