The spacing of ruled lines on a diffraction grating is 1900 nm.The grating is illuminated at normal incidence with a parallel beam of white light in the 400 nm to 700 nm wavelength band.The angular width of the gap between the first order spectrum and the second order spectrum is closest to:
A)3.3°
B)4.3°
C)5.3°
D)6.3°
E)2.3°

Question

Quizplus · Accepted Answer

The angular width between the first and second order spectra can be calculated using the diffraction grating formula: d(sin θ) = mλ. For the first order (m=1) and second order (m=2) spectra, calculate θ for the longest wavelength (700 nm) and shortest wavelength (400 nm) and find the difference. The calculations show that the angular width is closest to 3.3°.

The Spacing of Ruled Lines on a Diffraction Grating Is