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)
We know:
[tex]\theta_{1}=34\°[/tex]
In addition we are told the diffraction grating has 750 slits per mm, this means:
[tex]d=\frac{1mm}{750}[/tex]
Solving (2) with the known values we will find [tex]\lambda[/tex]:
[tex]\lambda=(\frac{1mm}{750})sin(34\°)[/tex] (3)
[tex]\lambda=0.00074559mm[/tex] (4)
Knowing [tex]1mm=10^{6}nm[/tex]:
[tex]\lambda=745.59nm[/tex] >>>This is the wavelength of the light, wich corresponds to red.
