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Particle Size and Diffraction Angles

The phenomenon of diffraction is observed when a specimen consisting of fine particles is illuminated with a beam of semi-coherent, collimated light. Good examples of this effect are a microscope slide containing particles of various sizes, and the spreading of automobile headlights on a foggy night. In both cases, diffraction is manifested through the scattering of light by small particles having linear physical dimensions similar to the wavelength of the illumination. This interactive tutorial demonstrates the effects of diffraction at an aperture and explores the spreading of light by a specimen composed of individual particles.

The tutorial initializes with a collimated beam of light containing planar wavefronts incident on an aperture of fixed size. The electric field of the wavefronts is disturbed by diffraction effects upon passing through the aperture to produce changes in the amplitude profile of the transmitted wavefronts. After leaving the slit, the deformed wavefronts encounter a microscope slide containing a linear series of particles, and are again diffracted at a divergent angle (represented in the tutorial as a red cone). In order to operate the tutorial, use the Particle Size slider to adjust the size of the individual particles between small, medium, and large. As the slider is translated to the right, the particle size increases, producing a corresponding decrease in the spreading angle (q) of the diffracted beam.

As previously mentioned, a very common example of diffraction occurs when light is scattered or bent by small particles having physical dimensions in the same order of magnitude as the wavelength of light. A good illustration is the spreading of automobile headlight beams by fog or fine dust particles. The amount of scattering and the angles taken by the redirected light beams are dependent upon the size and density of the particles causing the diffraction. Light scattering, a form of diffraction, also underlies the blue color of the sky and the often beautifully colored sunrises and sunsets that can be observed on the horizon. If the Earth were devoid of an atmosphere (lacking air, water, dust, and debris), the sky would appear black. When light from the sun passes through the Earth's atmosphere, volumes of gas molecules having varying densities, due to temperature fluctuations and the amount of water vapor present, will scatter the light. The shortest wavelengths (violet and blue) are scattered to the greatest extent, rendering the sky a rich, deep blue color. When there is a considerable amount of dust or moisture in the air, longer (primarily red) wavelengths also become scattered along with the blue wavelengths, causing the blue sky to become whiter in color.

When the sun is high (around noon) in a clear dry atmosphere, most of the visible light passing through the atmosphere is not scattered to a significant degree, and the sun appears almost white on a deep blue background. As the sun begins to set, the light waves must pass through increasing amounts of atmosphere, usually containing larger quantities of suspended dust and moisture. Under these circumstances, longer wavelengths of light become scattered and other colors start to dominate the color of the sun, which ranges from yellow to orange, finally turning red just before it drops below the horizon.

We can often observe pastel shades of blue, pink, purple, and green in clouds, which are generated by a combination of effects when light is refracted and diffracted from water droplets in the clouds. The amount of diffraction depends on the wavelength of light, with shorter wavelengths being diffracted at a greater angle than longer ones (in effect, blue and violet light are diffracted at a larger angle than is red light). The terms diffraction and scattering are often used interchangeably and are considered to be almost synonymous in many cases. Diffraction describes a specialized case of light scattering in which an object with regularly repeating features (such as a periodic object or a diffraction grating) produces an orderly diffraction pattern. In the real world, most objects are very complex in shape and should be considered to be composed of many individual diffraction features that can collectively produce a random scattering of light.

Contributing Authors

Douglas B. Murphy - Department of Cell Biology and Microscope Facility, Johns Hopkins University School of Medicine, 725 N. Wolfe Street, 107 WBSB, Baltimore, Maryland 21205.

Kenneth R. Spring - Scientific Consultant, Lusby, Maryland, 20657.

Matthew J. Parry-Hill and Michael W. Davidson - National High Magnetic Field Laboratory, 1800 East Paul Dirac Dr., The Florida State University, Tallahassee, Florida, 32310.



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