I had a few questions regarding the intensity graphs of fringe patterns observed when light is shone through a double slit vs a diffraction grating.

For a double slit, does the intensity of the fringes quickly decrease towards the outer maximas. I am relatively sure that this is true, however in some intensity graphs online, I saw a constant intensity like the below:


For some graphs, the intensity is constant like the one shown above, while for others it is not as shown below:


So which one is used when?



The intensity of the interference pattern of a double slit experiment is given by:

$$I(\theta) = \cos^2\left(\frac{\pi d \sin\theta}{\lambda} \right ) sinc^2 \left ( \frac {\pi b \sin\theta}{\lambda}\right)$$

with $b$ the width of the slits and $d$ the distance between the slits. See wikipedia for an derivation. The sinc function causes the the intensity to decrease as we move away from $\theta =0 $.

This would mean the second graph is the correct one. However, if we make the slits smaller and smaller, the dropoff towards the edges goes slower and slower. In the limit that $b \rightarrow 0$, the interference pattern becomes a pure cosine with no dropoff towards the sides and will look like the first figure.


If you look at the first link you posted it leads you to a page that exactly asks this. Sadly the answers are not openly avaliable.

But here on page 14-19 they calculate the answer. TL;DR: the intensity decreases towards the outer maxima.

Generally the second picture is the correct one, but with very closely spaced maxima one can approximate that over the central part the magnitude is constant. This is an approximation and needs to be tested in each case seperatelly: The approximation is equal to the approximation $cos^2(x) = 1$ for $x$ around 0.


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