Answer
0.878 cm.
Work Step by Step
See Figure 24-33A. Let the spacing between dark lines be āDā.
At the end of the plate, point A, where they are touching, we have dark band #0 (labeling each band by its m value, as given in Example 24-10). At the other end, near the wire, we have the dark band m=24, and then we have a distance of 0.5D until we reach the end of the plate. This is because, as derived in the Example, the area right next to the wire is bright.
Between the m=0 and m=24 dark band, we have a distance of 24D. When we add the half-spacing at the end of the plate with the wire, we have 24.5 spacings, which equals the length of the plates.
$$24.5D=21.5cm$$
$$D=\frac{21.5cm}{24.5}=0.878cm$$