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- For 2 slit
**diffraction**and gratings, constructive and destructive interference are determined byΔpath length = d sin θ = m or (m + 1/2) λ,

respectively, where d is the separation between slits (grating spacing), θ is measured from the normal to the slits and m is a non-negative integer:Note that since sin θ ≤ 1, m or (m + 1/2) must be ≤ d / λ.

- These applets demonstrates diffraction.
- For single slit diffraction, the intensity is
I

This can only be solved numerically for constructive interference, but for destructive interference we find the path length_{single}= I_{max}(sin(π a (sin θ) / λ) / (π a (sin θ) / λ))^{2}.Δpath length = a sin θ / (2 m),

where a is the slit width and m is a nonzero integer. This is equivalent to dividing the slit into an even number of parts, each of which acts as a point source.For double slit diffraction, the intensity is I

_{single}cos(π d (sin θ) / λ)^{2}, from which we retrieve the conditions above. - For diffraction in crystals, Δpath length = 2 d sin θ, where d is the lattice spacing. The factor of two comes from the fact that diffraction is taking place between two adjacent planes in the crystal.
- The smallest angle of
**resolution**(in radians) for a circular aperture is 1.22 λ / d, where d is the aperture diameter.

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©2010, Kenneth R. Koehler. All Rights Reserved. This document may be freely reproduced provided that this copyright notice is included.

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