If the geometry is such that the small angle approximation is valid, the width of the pattern is inversely proportional to the slit width. The sketches of the slit widths at right were scaled to the difference between the first minima of the diffraction patterns. where d is the distance from the source to mask, L is the distance from mask to image, w is the width of the slit and is the wavelength of the radiation. These single slit diffraction patterns were photographed with a helium-neon laser as the light source and a micrometer-controlled single slit. Single Slit Diffraction for Different Slit Widths Note: To obtain the expression for the displacement y above, the small angle approximation was used. His work set the stage for the development of. He also was the first to use extensively the diffraction grating, a device that disperses light more effectively than a prism does. The pattern below was made with a green laser pointer. Joseph von Fraunhofer, (born March 6, 1787, Straubing, Bavaria Germanydied June 7, 1826, Munich), German physicist who first studied the dark lines of the Sun’s spectrum, now known as Fraunhofer lines. The diffraction pattern at the right is taken with a helium-neon laser and a narrow single slit. If the conditions for Fraunhofer diffraction are not met, it is necessary to use the Fresnel diffraction approach. But an additional requirement is D> a 2/λ which arises from the Rayleigh criterion as applied to a single slit. Since the static kernel (typically the Fresnel kernel) doesn't change with shifts. Fraunhofer Diffraction Fraunhofer Diffraction GeometryĪlthough the formal Fraunhofer diffraction requirement is that of an infinite screen distance, usually reasonable diffraction results are obtained if the screen distance D > a. Fraunhofer Diffraction as Fourier Transform With the Fraunhofer approximation, diffraction is treated as a linear system with an impulse response characterized by some static kernel multiplied by a complex exponential with a linear phase proportional to the shift.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |