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Answer:
3.28 degree
Explanation:
We are given that
Distance between the ruled lines on a diffraction grating, d=1900nm=[tex]1900\times 10^{-9}m[/tex]
Where [tex]1nm=10^{-9} m[/tex]
[tex]\lambda_2=400nm=400\times10^{-9}m[/tex]
[tex]\lambda_1=700nm=700\times 10^{-9}m[/tex]
We have to find the angular width of the gap between the first order spectrum and the second order spectrum.
We know that
[tex]\theta=sin^{-1}(\frac{m\lambda}{d})[/tex]
Using the formula
m=1
[tex]\theta_1=sin^{-1}(\frac{1\times700\times 10^{-9}}{1900\times 10^{-9}})[/tex]
[tex]\theta=21.62^{\circ}[/tex]
Now, m=2
[tex]\theta_2=sin^{-1}(\frac{2\times400\times 10^{-9}}{1900\times 10^{-9}})[/tex]
[tex]\theta_2=24.90^{\circ}[/tex]
[tex]\Delta \theta=\theta_2-\theta_1[/tex]
[tex]\Delta \theta=24.90-21.62[/tex]
[tex]\Delta \theta=3.28^{\circ}[/tex]
Hence, the angular width of the gap between the first order spectrum and the second order spectrum=3.28 degree