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With a marginal difference of path of four semi-undulations we have a second extinction of the entire beam, because here the beam can be divided into four equal parts, every two of which quench each other. A second space of absolute darkness will therefore correspond to the obliquity producing this difference.
Corresponding, therefore, to an obliquity which produces a difference of three semi-undulations in the marginal waves, we have a luminous band, but one of considerably less intensity than the undiffracted central band.
The luminous intensity corresponding to this obliquity is a little less than one-half accurately 0.4 that of the undiffracted light. If the paths of the marginal waves be three semi-undulations different from each other, and if the whole beam be divided into three equal parts, two of these parts will, for the reasons just given, completely neutralize each other, the third only being effective.
If both series start at the same moment, one of them being, at starting, a whole wavelength in advance of the other, they also add themselves together, and we have an augmented luminous effect. The same occurs when the one system of waves is any even number of semi-undulations in advance of the other.
In this way we might proceed further, the general result being that, whenever the direction of wave-motion is such as to produce a marginal difference of path of an even number of semi-undulations, we have complete extinction; while, when the marginal difference is an odd number of semi-undulations, we have only partial extinction, a portion of the beam remaining as a luminous band.
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