We have a reflective grating with period 1400 nm and we are using it to study the spectrum of a multi-coloured light beam by diffracting the light onto an array of detectors Di to Da as shown in Figure 8. The beam is hitting the grating at an angle of O = 50°. Detector Di is meant to detect the longest wavelength (700 nm) and detector Da is for detecting the shortest wavelength (400 nm) and the detectors in between are for wavelengths in between 400 nm and 700 nm. What angles should detectors Di and D. be placed at (with respect to the vertical line) so that the spectrometer works as intended? Assume that we are working with the first diffraction order of the grating.

We have a reflective grating with period 1400 nm and we are using it to study the spectrum of a multi-coloured light beam by diffracting the light onto an array of detectors Di to Da as shown in Figure 8. The beam is hitting the grating at an angle of O = 50°. Detector Di is meant to detect the longest wavelength (700 nm) and detector Da is for detecting the shortest wavelength (400 nm) and the detectors in between are for wavelengths in between 400 nm and 700 nm. What angles should detectors Di and D. be placed at (with respect to the vertical line) so that the spectrometer works as intended? Assume that we are working with the first diffraction order of the grating.