A research group employs a diffraction grating with spacing d=1.7μm to separate the visible portion of a broadband source. They are concerned that overlap between different spectral orders will contaminate their measurements.
(a) For light of wavelength λblue=450nm in the second order (m=2), calculate the diffraction angle θ2,blue.
(b) For light of wavelength λred=700nm in the first order (m=1), calculate the diffraction angle θ1,red.
(c) Based on your answers to parts (a) and (b), determine quantitatively whether the second-order blue light overlaps the first-order red light. Show all reasoning.
(d) Suppose the grating spacing could be adjusted while keeping all other conditions fixed. Would decreasing d make the overlap problem better or worse? Explain your answer without additional calculations.