Intensity function of diffraction confusion

Question

In Feynman lecture 30 the light intensity function derived under Fraunhoffer conditions is of the form $$I=I_0\frac{sin^2(\frac{n\phi}{2})}{sin^2(\frac{\phi}{2})}$$ The way I understand it, the phi here represents the phase difference between light coming from two adjacent slits. This varies as a function of the angle theta to the central maximum, and is given by $$\phi=\frac{kd}{n}sin(\theta)$$ If the diffraction grating is such that one slit is of size d/n and there are n slits.

Now, what I am confused about is that this seems to disagree with the same intenstiy function given by James Nearing: $$I=I_0\frac{sin^2(\frac{kdsin\theta}{2})}{sin^2(\theta)}$$ Any help is much appreciated.

Answer 1

Feynman's formula is correct. I assume n is the number of slits. In Feynman's text $\phi$ is $k d \sin \theta$, where $d$ is the distance between two slits. I don't know James nearing.

http://www.feynmanlectures.caltech.edu/I_30.html