A student wishes to verify the manufacturer’s specification that a particular diffraction grating has 600lines/mm. She shines light from a sodium lamp (λ=589nm) perpendicularly onto the grating and measures the angle of the first bright line (m=1) to be θ=21.0∘.
Assume negligible experimental uncertainty for the purpose of calculation.
(a) Calculate the spacing d between adjacent slits in the grating. Provide your answer in micrometres.
(b) From your value of d, compute the number of lines per millimetre and state whether the grating meets the manufacturer’s claim. Show all steps.
(c) Determine the largest order mmax that could be observed for the sodium light with this grating before angles would exceed 90∘. Explain your reasoning.