Answer : The number of slits per millimeter marked on the grating are 238 slits/mm.
Explanation :
First we have to calculate the slit separation.
Formula used for a diffraction grating when maxima occur:
[tex]d\times \sin(a)=n\times \lambda[/tex]
where,
d = slit separation = ?
a = angle = [tex]24.0^o[/tex]
[tex]\lambda[/tex] = wavelength = 570.00 nm
n = order = 3
Now put all the given values in the above formula, we get:
[tex]d\times \sin(24.0^o)=3\times 570.00nm[/tex]
[tex]d=4204.19nm=4.20\times 10^{-3}mm[/tex]
Conversion used : [tex](1nm=10^{-6}mm)[/tex]
Now we have to calculate the number of slits per millimeter.
[tex]\text{Number of slits per millimeter}=\frac{1}{d}[/tex]
[tex]\text{Number of slits per millimeter}=\frac{1}{4.20\times 10^{-3}mm}[/tex]
[tex]\text{Number of slits per millimeter}=238.09slits/mm\approx 238slits/mm[/tex]
Therefore, the number of slits per millimeter marked on the grating are 238 slits/mm.
