To solve this problem it is necessary to apply the concepts related to destructive and constructive diffraction formulated in the bragg law.
It is understood by said law that,
[tex]n\lambda = dsin\theta[/tex]
where,
[tex]\lambda = wavelenght[/tex]
n = Any integer, representing the repetititon of the spectrum.
d = Width
[tex]\theta =[/tex] It is the angle between the incident rays and the dispersion planes.
PART A) For a diffraction of first order n=1, then
[tex]sin\theta = \frac{1*650*10^{-9}}{(\frac{0.012}{1000})}[/tex]
[tex]sin\theta= 0.0541[/tex]
[tex]\theta = sin^{-1}(0.0541)[/tex]
[tex]\theta = 3.105\°[/tex]
PART B) For a diffraction of second order n=2, then
[tex]sin\theta = \frac{2*650*10^{-9}}{(\frac{0.012}{1000})}[/tex]
[tex]sin\theta= 2*0.0541[/tex]
[tex]\theta = sin^{-1}(2*0.0541)[/tex]
[tex]\theta = 6.21\°[/tex]
Therefore the angles of the first two diffraction orders are 3.1° and 6.2°
