Suppose a $2\mathrm{.}00-$cmcm$-$wide diffraction grating with $800$ lines$/$mmmm is $0\mathrm{.}500$mm in front of a detector, forming a simple version of a "half$-$meter spectrometer." A spectrometer is used to measure the wavelengths of light by spreading them out across a detector. The quality of a spectrometer is its ability to distinguish or resolve two very similar wavelengths. A simple double slit has very poor resolution because the fringes are very wide; thus the interference patterns of two similar wavelengths would be so overlapped that you couldn$$t distinguish them. A diffraction grating with many slits creates much narrower interference fringes, allowing two similar wavelengths to be distinguished by where their fringes fall on the detector. What is the minimum difference between two wavelengths that this spectrometer can resolve? What is minmin$,$ the minimal resolvable wavelength difference, for this half$-$meter spectrometer for two nearly identical wavelengths at $500$ nmnm$.$