Chapter 37, Problem 49AP

Two closely spaced wavelengths of light are incident on a diffraction grating. (a) Starting with Equation 37.7, show that the angular dispersion of the grating is given by

$\frac{d\theta }{d\lambda }=\frac{m}{d\cos \theta }$

(b) A square grating 2.00 cm on each side containing 8 000 equally spaced slits is used to analyze the spectrum of mercury. Two closely spaced lines emitted by this element have wavelengths of 579.065 nm and 576.959 nm. What is the angular separation of these two wavelengths in the second-order spectrum?