A diffraction grating with an unknown line spacing is illuminated simultaneously by…
PHYSICS · Multi-part · AP · Physics 2: Algebra-based · Waves Sound and Physical Optics · Waves Sound and Physical Optics
Problem
A diffraction grating with an unknown line spacing is illuminated simultaneously by red light of known wavelength λr=650nm and violet light of unknown wavelength λv. The first-order maxima (m=1) for the two colours are observed at angles θr=22.5∘ and θv=19.2∘ relative to the normal.
Assume the small-angle approximation is not justified for these measurements.
(a) Determine the line spacing d of the grating. Give your answer in nanometres to three significant figures.
(b) Using the value of d from part (a), calculate the wavelength λv of the violet light. Express your answer in nanometres to three significant figures.
(c) Both colours are now observed in second-order (m=2). Predict the two angles at which their second-order maxima will appear and comment on whether any overlap of colours is expected at that order.
(d) Give one practical reason, based on your results, why diffraction gratings are preferred over double slits when separating multiple wavelengths in laboratory spectroscopy.