Q3. A scanning Fabry-Prot (F-P) spectrometer (Fig. 3-1) consists of two R=99.5% refection mirrors separated in air. The pinhole followed by a collimating lens ensures normal incidence of light on the mirror surfaces. The spectrometer is required to measure (unambiguously) in the spectral range of 587.0 588.5 nm, and is required to resolve the three emission lines of a helium source, which are at 587.5615 nm, 587.5640 nm, and 587.5966 nm. R R Emission Source det. pinhole d is scanned pinhole Fig. 3-1 A scanning Fabry-Perot spectrometer. (a) [1 mark] Find the required minimum resolving power of the spectrometer. (b) [1 mark] Find the required minimum free-spectral range. Express it in THz. (c) [1 mark] What is the finesse of the F-P spectrometer? (d) [2 marks] What is the acceptable range for the separation d? (e) [1 mark] As we scan d, suppose we have detected a group of three closed spaced peaks corresponding to the three emission lines, at d, d2, and dz, respectively. If A12=d-d, and A23=d3-d2, find the ratio A23/ A12. A 50-mm-wide transmission grating, with 1000 lines/mm, is used as a diffraction spectrometer to replace and improve on the F-P spectrometer in both free-spectral range and spectral resolution. The same light source illuminates the diffraction grating at normal incidence as shown in Fig. 3-2, below: Emission Source | D pinhole Diffraction Grating Fig. 3-2 Incident light is collimated by the lens to a beam of width D (f) [1 mark] Which order of diffraction may be used to resolve all three wavelengths? (g) [1 mark] Fine the minimum beam width D (Fig. 3-2) for case (f). (h) [1 mark] Given the focal length of the lens f = 20 cm, what is size of the pinhole that will guarantee the beam to be spatially coherent across its width, D