For a diffraction grating in which all the surfaces are normal to the incident radiation, most of the energy goes into the zeroth order, which is useless from a spectroscopic point of view since in zeroth order all the wavelengths are at 0°. Therefore, modern gratings have shaped, or blazed, grooves as shown in Figure. This shifts the specular reflection, which contains most of the energy, from the zeroth order to some higher order.

(a) Calculate the blaze angle ф in terms of a (the groove separation), λ (the wavelength), and m (the order in which specular reflection is to occur).

(b) Calculate the proper blaze angle for the specular reflection to occur in the second order for light of wavelength 450 nm incident on a grating with 10,000 lines per centimeter.