In a double slit experiment, it is not necessary for the slit width to be smaller than the slit separation, but it is often the case for obtaining the most pronounced interference pattern.
The interference pattern in a double slit experiment is formed by the interference of light waves that pass through the two slits. The condition for observing a well-defined interference pattern is that the coherent waves from the two slits interfere constructively or destructively.
If the slit width is much larger than the slit separation, the individual slits behave more like sources of light, producing separate diffraction patterns. In this case, the interference pattern becomes less distinct.
On the other hand, when the slit width is smaller compared to the slit separation, the individual diffracted waves from each slit overlap more significantly, resulting in a clearer and more pronounced interference pattern.
So, while it is not a strict requirement for the slit width to be smaller than the slit separation, it is generally preferred to achieve a well-defined interference pattern in a double slit experiment.