Past exam of the physics 2 paper of the University of Oxford / 2014 resit / 5

For normal incidence, the first-order maximum of a diffraction grating obeys $s\sin \theta =\lambda$. Differentiating at ${\lambda }_0$ givesTherefore the positive first-order peaks are separated byThe larger wavelength is diffracted farther from the normal. Both first orders must exist, ${\lambda }_0+\delta \lambda <s$; extremely close to grazing incidence the finite difference of the two inverse sines should replace this local approximation.