What is the spacing between slits of the grating?

Question

A helium-neon laser (wave length=633nm) illuminates a diffraction grating. The distance between the two m=1 bright fringes is 32 cm on a screen 2.0 m behind the grating.

Answer 1

Using the law of cosines, the total angle between fringes is arccos(1-32^2 / 2*200^2) = 9.177º

Half this angle is ø in the formula

d*sinø = lambda

d = 633*10^-9/ sin(9.177º/2) = 7.9*10^-4 cm