Fraunhofer Diffraction Proving

relinquished™

I am to prove that in

y = R * m * (wavelength) / a

where y is the distance between two minima, a is the width of the slit, R is the length between the screen and the slit grating, and m is an integer which is the order of the minima.

I know I have to use the paraxial approximation where tan x is approximately sin x which is approx. x, but I can't seem to apply it. When I refer to my textbooks, they state that y is the difference between the central maximum and the first minimum when m=1. Is this applicable bet. two minima as well?

Claude Bile

Start with the condition for constructive interferance;

dsin(theta) = m(lambda)

Then apply the small angle approximation. It is quite simple.

Your textbook is referring to y as the difference between the first maximum and the centre of the pattern, which is equivalent (within the small angle approximation) to the distance between successive minima.

Claude.