All Problems Diffraction of Light
Problem 5.134
A transparent diffraction grating has a period \(d=1.50 \mu \mathrm{m}\). Find the angular dispersion \(D\) (in angular minutes per nanometres) corresponding to the maximum of highest order for a spectral line of wavelength \(\lambda=530 \mathrm{nm}\) of light falling on the grating (a) at right angles; (b) at the angle \(\theta_{0}=45^{\circ}\) to the normal.
5.134. (a) \(D=k / d \sqrt{1-(k \lambda / d)^{2}}=6.5\) ang. min/nm, where \(k=2\); (b) \(D=k / d \sqrt{1-\left(k \lambda / d-\sin \theta_{0}\right)^{2}}=13\) ang. min/nm, where \(k=4\).