Answer: 31.33 degrees
Explanation:
The diffraction angles [tex]\theta_{n}[/tex] when we have a slit divided into [tex]n[/tex] parts are obtained by the following equation:
[tex]dsin\theta_{n}=n\lambda[/tex] (1)
Where:
[tex]d[/tex] is the width of the slit
[tex]\lambda[/tex] is the wavelength of the light
[tex]n[/tex] is an integer different from zero.
Now, the first-order diffraction angle is given when [tex]n=1[/tex], hence equation (1) becomes:
[tex]dsin\theta_{1}=\lambda[/tex] (2)
Now we have to find the value of [tex]\theta_{1}[/tex]:
[tex]sin\theta_{1}=\frac{\lambda}{d}[/tex]
[tex]\theta_{1}=arcsin(\frac{\lambda}{d})[/tex] (3)
We know:
[tex]\lambda=104nm=104(10)^{-9}m[/tex]
In addition we are told the diffraction grating has 5000 slits per mm, this means:
[tex]d=\frac{1mm}{5000}=\frac{1(10)^{-3}m}{5000}[/tex]
Substituting the known values in (3):
[tex]\theta_{1}=arcsin(\frac{104(10)^{-9}m}{\frac{1(10)^{-3}m}{5000}})[/tex]
[tex]\theta_{1}=arcsin(0.52)[/tex]
Finally:
[tex]\theta_{1}=31.33\º[/tex] >>>This is the first-order diffraction angle
