# Is the $n$ in the single slit diffraction equation for dark fringes any integer or specifically odd integers?

The equation for angular positions of dark fringes due to single slit diffraction is $$a \sin(x) = n \lambda$$ correct? My question is on that $$n$$. I read that it takes integer values which give the order of the dark fringe. But in deriving that equation they said the path difference is given by $$0.5 a \sin(x)$$ and that it should equal a whole number of HALF wavelengths for there to be destructive interference resulting in a dark fringe. But if the $$n$$ in the final equation takes an even value, e.g 2 or 4, won't the path difference be a whole number of EVEN wavelengths instead? Causing a bright fringe?

• You can write different expressions for this, with the constraints on $n$ depending on how you write it. I usually use one in which $n \in \mathbb{Z}$. Commented May 9, 2018 at 21:39
• So in that form where "asin(x) = n*lambda" what are the constraints on n? Can it take an even value? Commented May 9, 2018 at 21:52
• You should edit that into your question, but you should also be able to answer it yourself. Commented May 9, 2018 at 21:55