When you put different plates into the lamp, the spacing between the light points changed. This has to do with interference. Light propagates through space like a wave and can therefore interfere like a wave. When two waves interfere constructively, they result in a bigger wave, while destructive interference results in a smaller total wave.
(source: https://kids.britannica.com/students/article/wave/628468/media)
This depends on whether a wave is in or out of phase. When two identical waves interfere, the phase difference depends only on the optical path difference. This is basically how far a ray of light has travelled. When a wave interacts with an obstacle, it behaves in a complicated way, too advanced to describe here in detail. The important result is, however, that the ray is bent. This means that the rays coming from different slits together in a single point have a path difference.
Therefore, an optical path difference exists and interference occurs. If the amount of slits is large enough, the result will only be individual spots of illumination. The spacing between these spots depends on the spacing between the slits.