Find the maximum number of lines per centimeter a diffraction grating can have and produce a first-order maximum for the largest wavelength of visible light. (assume the wavelengths of visible light range from 380 nm to 760 nm in a vacuum.)

To solve this problem it is necessary to apply the concepts related to constructive interference for multiple split.

The precaution is given by,

Where,

d = Distance between the slits

Angle between the path and a line from the slits to the screen

m = Any integer, representing the number of repetition of the spectrum.

Wavelength

For first order equation we have that m = 1 then

As the maximum number of lines corresponds to the smallest d values, we have that

Therefore the maximum numbers of lines per centimeter would be

The maximum numbers of lines per centimeter is 13158