# Vertical interference in double-slit

Why is no interference pattern in the vertical axis in a double-slit ? Isn't a vertical slit just thousands of small slits one next to the other ? So shouldn't this create an interference pattern also along the vertical axis ?

• The vertical dimension is usually too big. Had it been comparable to the slit width you would have obtained an interference along that dimension too. – Raziman T V Jan 8 '17 at 3:44

We can construct such a one-dimensional function as a square function that represents the slit convolved by a comb function $$h(y/w) \otimes C_d(y)$$ where $h(y/w)$ is the is the square function of width $w$ and $C_d(y)$ is a comb function consisting of impulse functions separated by $d$.
The Fourier transform of this is given by the product of the Fourier transform of the square function, which is a sinc function $${\rm sinc}(wu) = \frac{\sin(\pi wu)}{\pi wu}$$ and the Fourier transform of the comb function, which is again a comb function, but where the impulses are separated by $1/d$. Note that the sinc function has zeros where $u=n/w$ for any integer $n$ not equal to zero.