To solve this problem it is necessary to apply the concepts related to the principle of superposition and the equations of destructive and constructive interference.
Constructive interference can be defined as
Where
m= Any integer which represent the number of repetition of spectrum
= Wavelength
d = Distance between the slits.
= Angle between the difraccion paterns and the source of light
Re-arrange to find the distance between the slits we have,
Therefore the number of lines per millimeter would be given as
Therefore the number of the lines from the grating to the center of the diffraction pattern are 380lines per mm