Sunday, November 28, 2010

Physics Concept: Diffraction Grating

Diffraction is an incident where the wave is maximized at the shore of the narrow slit and light resistor. Light is not more traveling by the straight line path, and this case is causing the light interference so that image at the shore of the light resistance is noisy. The diffraction also limits the small-size of the seen object and the accuracy of the measurement.

If a ray is parallel with the wave length λ that is directed perpendicularly to the s size of a gap, it will be created is the pattern of diffraction behind of the gap. In the angles of θn (calculated to direction of incoming ray), there will be the dark gaps if:

where n = 1,2,3,... show the dark region.
Diffraction also caused the resolution limits of two objects. When we observe two contiguous objects by an optic tool, so the diffraction pattern that is caused by the aperture, will limit our ability to differentiate the objects. In order to see the both of objects separately, the angle of θ that is created on the object ought to more than the critical angle of θc, as formula:

where D is the diameter of diaphragm, and λ is the length of light wave.
Shortly, it will be impossible to see an object that smaller than the wave length of used light.
The diffraction grating consist to parallel and identical slits in the great numbers with the distance between slits is named as constant d. If the wave by length λ is directed perpendicularly to the grating by constant d, it will be created the light region beside the split with θn (according to the direction of incoming ray), as formula:

where n = 1,2,3,…show the order of light diffraction.
This equation also obeys in the maximum main line on the interference pattern with two and three slits. The diffraction pattern will be more complex, if the slits are large enough so there are some minimum lines in the pattern of single-split diffraction.
Let us consider a common situation that of light passing through a narrow opening modeled as a slit, and projected onto a screen. To simplify our analysis, we assume that the observing screen is far from the slit, so that the rays reaching the screen are approximately parallel. This can also be achieved experimentally by using a converging lens to focus the parallel rays on a nearby screen. In this model, the pattern on the screen is called a Fraunhofer diffraction pattern.

Figure.1. (a) Fraunhofer diffraction pattern of a single slit. The pattern consists of a central bright fringe flanked by much weaker maxima alternating with dark fringes. (Drawing not to scale.) (b) Photograph of a single-slit Fraunhofer diffraction pattern.
Because light beam contains only a single wavelength, then only one pair of spots that appear on the screen on each order. But if the experiment is performed with light of five colors, then there are couple spots in each order a number of wavelengths contained in the light of the source. The diffraction angle θ  for each wavelength is given by equation (1). We will look at results like this when using white light from incandescent lamp instead of laser light. If the distance between the screen and slit spacing l and n bright of light into the center is p, then the equation for the light to n is: