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1. The goals of experiment
- illustration of the Fraunhoger diffraction by using a parallel beam and a diffraction grating
- determination of wavelength of a monochromatic light radiation
2. Theoretical aspects:
2.1 Fraunhofer diffraction through a slit
Let’a consider a rectangular slit of length L>>width a. (fig.1). Through the slit passes a plane wave with the propagation direction situated in a normal plane on the slit and parallel with a.
Fig. 2
The wave will be diffracted along all the angles formed with the slit normal, beween .
The expression of the resultant wave is obtained by integrating the contribution of all secondary sources from the slit plane. This is:
where is the mathematical expression of the resulting plane wave, k is the modulus of the wave vector and is the angular frequency.
The intensity of the light diffracted is computed, by definition, by multiplication of * with :
The curve I = I() is shown in Fig. 3.
It is noticed that the intensity of the light diffracted reaches minima (nulls) when: sin = 0 (with 0), therefore when = m (m = 1, 2, 3...) or :
asin = m (3) .
In order to determine the other maximal values for I() (besides the principal maximum when = 0) the following condition must be fulfilled:
having solutions the roots of the transcendental equation tg = , that are : =0 ; 1,43 , 2,46 , etc.
Passing at the independent variable results, for the maximum condition, the expression:
asin=n , cu n = 0 ; 1,43 ; 2,46 ...... (4)
From (3) results that the first minimum appears when is satisfied the condition:
- Therefore, when a>>, is very small (negligible) and the diffraction image reduces to the image of the slit.
- When it has the same order of magnitude with , the diffraction image becomes more proeminent, the principal maximum becoming less and less sharp.
- When a = , = /2 , the central maximum is on the whole field
- When a << no diffraction is obtained
2.2. Fraunhofer diffraction through a parallel beam and a diffraction grating
A one dimensional diffraction grating consists in a system of rectangular slits parallel, equal and equidistant. A slit of this grating has a rectangular shape, with the width l smaller than the length L. (fig. 4)
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