= Solution
A $5.0\,\mathrm{mm}$ beam illuminates $N=5.0\,\mathrm{mm}/p=1000$ slits. The <resolving power of a diffraction grating> in order $m=3$ is $mN=3000$, corresponding to a <Rayleigh criterion> separation $\delta\lambda_R\simeq460/3000=0.153\,\mathrm{nm}$. The $0.5\,\mathrm{nm}$ separation therefore gives \b[two well separated main peaks]. The <finite-grating incoherent doublet profile> adds the mutually incoherent lamp <intensities>, not their amplitudes.
\Image[/past-exam-of-the-physics-a-course-of-the-university-of-cambridge/2011/paper-1-grating-doublet.png]
{title=Third-order doublet for two illuminated grating widths}
{description=Original finite-N intensity sums, with equal line strengths and narrow slits. The horizontal coordinate is the wavelength inferred from the third-order grating equation. Each component is dashed and their incoherent sum is solid.}
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