Lens Diffraction

The term diffraction in the case of waves refers to their bending round the obstacles. When the obstacle is large compared to the wavelength no wave bends round the edges of the obstacle. When the size of the obstacle is small compared to the wavelength of the light wave bend round the edges of the obstacle. When the size of the obstacle is very very small the waves bend round it so that we find no practical effect on the wave.

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The diffraction phenomena is more predominant when the size of the obstacle is small and is comparable with the wavelength of the incident light. Ex : When a beam of light passes from a narrow slit it spreads out to certain extent in the geometrical shadow. Diffraction can be explained by Huygens - Fresnel principle. According to this principle each point on an unobstructed wavefront acts as a source of secondary waves. The secondary sources are mutually coherent and the waves emitted by them interfere to produce diffraction patterns. The amplitude at any arbitrary point in space due to the secondary wave depends on the angle between the outward drawn normal to the wavefront and the line joining the wavefront and the point P.

Fraunhofer Diffraction Using Lens

There are two approaches to explain diffraction. The first is Fresnel diffraction ( a general approach) and the second is Fraunhofer diffraction ( a simplified approach). Here we discuss about the lens diffraction by Fraunhofer.

In this approach the source of light and the screen are considered to be at infinite distances from the obstacle or aperture. The wave fronts involved are plane wavefronts. Lenses are used to observe diffraction pattern. It can be said that Fraunhofer diffraction is the limiting case of Fresnel diffraction. Mathematical treatment of Fraunhofer diffraction is simple. Let us briefly consider diffraction from a single slit as an example for Fraunhofer approach. In the figure below, a plane wavefront illuminates a slit of width d. A converging lens between the slit and the screen is used to focus diffraction pattern on the screen. The area of the incident wavefront on the slit is divided into elementary zones of width of dx, parallel to the edges of the slit. The secondary waves emitted by each zone superpose at point P on the screen. The resultant intensity at P is determined by the angle `theta` , the angle of diffraction, and the amplitude of the oscillation produced by different zones.

The amplitude of the oscillation produced by a zone depends only on the area of the zone. The area of the zone is proportional to the width (dx) of the zone. Therefore amplitude 'dA' due to an oscillation produced by a zone of width dz oscillation produced by a zone of width dx at any point on the screen will have the form dA = C dx, C is a constant. The algebraic sum of the amplitudes of the oscillations due to all the zones at a point on the screen determines the intensity of the diffraction pattern.Applications of Lens Diffraction1. The wavelengths of either monochromatic or composite ratdiations can be measured accurately by diffraction technique using diffraction grating.

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2.The wavelengths of X-rays are determined by X-ray diffraction.3. Structures of crystalline solids are determined by X-ray , electron and neutron diffraction measurements.4. Velocity of sound in liquids (organic and inorganic) can be estimated with the help of ultrasonic diffraction techniques.5. Ultrasound scanning uses the principle of diffraction to assess the size and shape of ulcers, tumours etc., in human body.