Respuesta :
The destructive interference formula for diffraction grating problems is [tex]d\ sin(\theta) = (n+\dfrac{1}{2} )\lambda[/tex].
What is destructive interference?
When the maxima of two waves are 180 degrees out of phase, destructive interference occurs: a positive displacement of one wave is cancelled exactly by a negative displacement of the other wave. The resultant wave has zero amplitude.
In a diffraction grating, the formula for brighter patches arising from constructive interference and darker patches arising from destructive interference is:
[tex]d\ sin(\theta) = n\lambda[/tex]
Here, d is the grating spacing, θ is the angle of light, n represents the fringe order, and w denotes the wavelength.
The value of N can only be integers values.
Now, Because destructive interference occurs between the fringes, the destructive interference formula is
[tex]d\ sin(\theta) = (n+\dfrac{1}{2} )\lambda[/tex]
where n is again an integer.
Hence, the destructive interference formula for diffraction grating problems is [tex]d\ sin(\theta) = (n+\dfrac{1}{2} )\lambda[/tex].
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