Question

define variables in sin(theta)= (n * lamda)/d for Chemical grating, Emission spectra

Answer 1

That equation is actually the following:

d sin = n

This formula means: path difference of two light rays = n

where n is an interger of lambda, and lambda is the wavelength of a coherent source. Path difference = n times wavelength of light in this case ensure constructive interference, giving you the bright spots on the screen. the path difference is between two rays scattered/reflected off two adjacent gratings (on a piece of metal or something) so the typical experimental set up is you have a laser of some fixed but unknown wavelength, you shine the beam on an object with gratings (should be spaced uniformly with fixed distance between gratings of d).

Using this formula, you can get two kind of fringes, a bright one and a dark one; Bright fringes occur at points of constructive interference. This happens when the path difference between the waves is nλ (where n = 0, 1, 2...); Dark fringes occur at points of destructive interference; this happens when the path difference is nλ/2 (where n = 1, 2, 3...).