Laboratoare optică cu date prelucrate

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 :

asin = 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:

asin=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)