Fraunhofer Diffraction Geometry

Although the formal Fraunhofer diffraction requirement is that of an infinite screen distance, usually reasonable diffraction results are obtained if the screen distance D >> a. But an additional requirement is D>> a2/λ which arises from the Rayleigh criterion as applied to a single slit. If the conditions for Fraunhofer diffraction are not met, it is necessary to use the Fresnel diffraction approach.

The diffraction pattern at the right is taken with a helium-neon laser and a narrow single slit. The pattern below was made with a green laser pointer.

Note: To obtain the expression for the displacement y above, the small angle approximation was used.

Calculation for single slit
Intensity for single slit
Double slit interference
Comparison to double slit
Examine approximation
Variation with slit width
Index

Diffraction concepts

Fraunhofer diffraction

Oxford Optics
 
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Single Slit Diffraction for Different Slit Widths

These single slit diffraction patterns were photographed with a helium-neon laser as the light source and a micrometer-controlled single slit. The sketches of the slit widths at right were scaled to the difference between the first minima of the diffraction patterns. If the geometry is such that the small angle approximation is valid, the width of the pattern is inversely proportional to the slit width.

Calculation for single slit
Intensity for single slit
Double slit interference
Comparison to double slit
Examine approximation
Index

Diffraction concepts

Fraunhofer diffraction
 
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