Final answer:
The provided question seems to be about MRI k-space lines, but the information included is regarding diffraction gratings and light interference patterns. The concepts are not directly related, and the initial query would require context specific to MRI image reconstruction and data acquisition.
Step-by-step explanation:
The question appears to be related to magnetic resonance imaging (MRI), more specifically, to k-space, which is used in MRI to encode spatial frequencies for image reconstruction. The line of k-space mentioned relates to the data acquisition process in MRI, where the same line can be filled multiple times to improve the signal-to-noise ratio or for other imaging purposes. However, the additional information provided seems to be related to the diffraction grating equations for interference patterns and splitting of light, not directly related to filling lines of k-space per slice in MRI.
The specific question asked does not align with the additional information given, which involves concepts like interference, diffraction gratings, and the wavelength of light (d sin θ = mλ). The diffraction grating part discusses the maximum number of lines per centimeter a diffraction grating can have to produce a complete first-order spectrum for visible light. For a diffraction grating with 10,000 lines per centimeter, each line is separated by 1/10,000 of a centimeter, and using the formula, different diffraction patterns can be analyzed.