Answer:
Angle of first order maximum, [tex]\theta=21.19^{\circ}[/tex]
Explanation:
Given that,
Wavelength of the light, [tex]\lambda=452\ nm=452\times 10^{-9}\ m[/tex]
Number of lines, N = 8000 per cm
The relation between the number of lines and the slit width is given by :
[tex]d=\dfrac{1}{N}[/tex]
[tex]d=\dfrac{1}{8000/cm}[/tex]
[tex]d=0.000125\ cm=1.25\times 10^{-6}\ m[/tex]
The equation of grating is given by :
[tex]d\ sin\theta=n\lambda[/tex]
n = 1
[tex]sin\theta=\dfrac{\lambda}{d}[/tex]
[tex]sin\theta=\dfrac{452\times 10^{-9}}{1.25\times 10^{-6}}[/tex]
[tex]\theta=21.19^{\circ}[/tex]
So, the angle of the first-order maximum is 21.19 degrees. Hence, this is the required solution.
