Intensity of a grating pattern in the limit of infinite slits

$$Ipropto frac{sin^2(Ndelta)}{sin^2(delta)}$$

Where $N$ is the number of slits and $delta$ contains the angle, wavelength and slit spacing dependence. In the limit as $delta to 0, I to N^2$. This makes sense because as $N$ increases the sharpness of the maxima increases and therefore we expect that the intensity of the maxima should increase to conserve energy.

But what about the limit as $Ntoinfty$ (as slit spacing remains constant)? Would we say that the maxima tend to delta functions or something like that? Although that may fit the pattern it does seem troubling because if we were to have a very long grating in a lab surely we wouldn’t expect to see such high intensities.

So what is the true dependence of the intensity of the central maximum on $N$ as $N$ becomes very large?