Answer:
(a) angles of maxima = 13.9°, 28.7° , 46°, 73.7° on either side
b] largest order = 4
Explanation:
(a) for diffraction maxima,
[tex]sin \theta =m\times \lambda/d[/tex]
Here, m is the order, [tex]\lambda[/tex] is the wavelength, [tex]\theta[/tex] is the angle at which maxima occur, d is inter planar spacing.
And we know that lines per mm (N) is related with d as,
[tex]N=\frac{1}{d}[/tex]
Given that the wavelength is,
[tex]\lambda=600.0 nm=600\times 10^{-9}m[/tex]
And [tex]N=\frac{400 lines}{mm} \\N=\frac{400 lines}{10^{-3}m }[/tex]
Now,
[tex]sin \theta =m\times \lambda\times N[/tex]
Therefore,
[tex]sin \theta= m\times600\times 10^{-9} \times 400\times 10^{3}\\sin \theta=0.24m[/tex]
Here, m can be 1,2,3,4 as sin theta has to be less than 1.
[tex]\theta = arcsin 0.24 , arcsin 0.48 , arcsin 0.72 , arcsin 0.96[/tex]
Therefore, angles of maxima = 13.9°, 28.7° , 46°, 73.7° on either side
b] largest order = 4
