To solve this problem it is necessary to apply the concepts related to constructive interference for multiple split.
The precaution is given by,
[tex]dsin\theta = m\lambda[/tex]
Where,
d = Distance between the slits
[tex]\theta =[/tex] Angle between the path and a line from the slits to the screen
m = Any integer, representing the number of repetition of the spectrum.
[tex]\lambda =[/tex]Wavelength
For first order equation we have that m = 1 then
[tex]d sin\theta = \lambda[/tex]
As the maximum number of lines corresponds to the smallest d values, we have that [tex]\theta = 90[/tex]
[tex]d sin90=\lambda[/tex]
[tex]d = 760nm[/tex]
Therefore the maximum numbers of lines per centimeter would be
[tex]N = \frac{10^{-2}m}{d}[/tex]
[tex]N = \frac{10^{-2}m}{760*10^{-9}m}[/tex]
[tex]N = 13157.89[/tex]
The maximum numbers of lines per centimeter is 13158
