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Diffraction of Light

Problem 5.134

A transparent diffraction grating has a period d=1.50μmd=1.50 \mu \mathrm{m}. Find the angular dispersion DD (in angular minutes per nanometres) corresponding to the maximum of highest order for a spectral line of wavelength λ=530nm\lambda=530 \mathrm{nm} of light falling on the grating (a) at right angles; (b) at the angle θ0=45∘\theta_{0}=45^{\circ} to the normal.

Reveal Answer
5.134. (a) D=k/d1−(kλ/d)2=6.5D=k / d \sqrt{1-(k \lambda / d)^{2}}=6.5 ang. min/nm, where k=2k=2; (b) D=k/d1−(kλ/d−sin⁡θ0)2=13D=k / d \sqrt{1-\left(k \lambda / d-\sin \theta_{0}\right)^{2}}=13 ang. min/nm, where k=4k=4.
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