Final answer:
The assumption that is NOT made when deriving diffraction patterns is ignoring the width of the slits; rather, it is an essential factor affecting the diffraction and resulting interference pattern.
Step-by-step explanation:
When deriving the single and double slit diffraction patterns, we make several assumptions. Among these are that the slits are uniformly illuminated, the light from the slits is coherent, the screen is placed a long way from the slits, and that light behaves as a wave. It is true that the slits are assumed to be uniformly illuminated and that the light source is coherent. Moreover, the assumption that the screen is far enough to consider rays coming from the slits to be nearly parallel is also made. However, one of the assumptions we don't make is that we can ignore the width of the slits. In fact, the width of the slits is not ignored because it affects the diffraction and hence the interference pattern that is projected onto the screen.
When the width of the slits is similar to the wavelength of the light used, diffraction is significant and cannot be ignored as it impacts the resulting pattern of maxima and minima on the screen. As addressed in provided references, Young's double-slit experiment and subsequent studies on diffraction consider the effects of slit width as a contributing factor to the overall interference pattern.