A grating $25$ mm wide, with $1200$ lines per millimeter, is illuminated with collimated light at normal incidence. The grating is illuminated with a wide range of wavelengths in the visible regime, from $500$nm to $600$ nm $.$

a$)$ Calculate the diffraction angle for orders $\backslash (\backslash$mathrm$\{$m$\}=0,1\backslash ),$ and $2.[6$ points$]$

b$)$ Sketch the diffraction pattern for the wavelength range. Which, if any, diffraction orders overlap? $[4$ points$]$

c$)$ Describe why one would want to use a blazed grating over a grating with a slit profile? $[2$ points$]$