The destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].
Destructive interference happens when the maxima of two waves are 180° out of phase a positive displacement of one wave is canceled exactly by a negative displacement of the other wave.
The formula for brighter patches resulting from constructive interference and darker patches resulting from destructive interference in a diffraction grating is:
[tex]\rm d sin \theta = n \lambda[/tex]
The grating spacing is denoted by d, the angle of light is denoted by a the fringe order is denoted by n, and the wavelength is denoted by [tex]\rm \lambda[/tex].
The destructive interference formula is now based on the fact that destructive interference occurs between the fringes.
Hence the destructive interference formula for diffraction grating problems is [tex]d sin \theta = (n+\frac{1}{2})\lambda[/tex].
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