Click and drag  to change the values of applet parameters.
 


E0- amplitude of the incident wave.
 

F1(q) - spatial spectral amplitude of the wave diffracted by the individual slit.

FN(q) - multiple beam interference factor describing the cooperative action of all slits.

The final plot I(q)/I m= F1(q)*FN(q) is the pattern of a plane wave diffracted by a rectangular amplitude grating.

The width of the central fringe on blue graph is Dq=l /Nd, (angular width of principal maxima).

The light intensity at maxima is Imax=Im*N2. The total number of principal maxima is M = d/l.

Diffraction Grating Experiment


In the applet below, the blue graph represents the FN(q) function.
The green graph is the F1(q) function.
The red graph is the I(q)/Im function.

Diffraction by periodic structures.

The diffraction of light by periodic structures is applied for optical wave-length measurements and for analysis of the spectral composition of radiation.

    Diffraction grating.

    A diffraction grating represents a spatial periodic structure, the interval of which is comparable to the optical wave length. There are transmitting and reflecting, as well as amplitude and phase diffraction gratings. The transmitting gratings transmit light, while the reflecting ones reflect it. The simplest amplitude transmitting grating consists of a system of slits in an opaque screen. The reflecting amplitude gratings are produced by ruling lines on a plane or concave mirror.

    The physics of light diffraction by a grating.

    The elementary theory of light diffraction by a grating can be presented on the basis of the Huygens-Fresnel ideas about secondary wavelets interference. The incident optical wave produces in the slits coherent sources of secondary wavelets. The resulting optical field is formed by superposition and interference of these waves. The wave front intersection point, i.e. the points at which the fields add in phase, align in straight lines, forming a discrete set of directions along which the secondary wavelets reinforce one another. These are in the direction in which the principal maxima of the diffraction pattern are formed (Red line on the screen). Along any other direction, the secondary wavelets interfere destructively, i.e. the phase relations between the waves are such that waves suppress each other. As a result, the narrow principal maxima of the diffraction pattern turn out to be separated by broad dark gaps.

    The equation of diffraction grating.

Using Fresnel’s idea about the interference of secondary wavelets, it is easy to find the directions to the principal maxima of the diffraction pattern. These are the directions for which the path difference of the beams from adjacent slits is a multiple of the wavelength. It can be seen from Fig.2 that path difference between the rays coming in the direction Q from two adjacent slits of the grating is equal to d sin Q. Consequently, the directions of principal maxima are determined by equation:

dsinq = ml, m = 0,±1,±2,...

where l is the optical wavelength. The equation allows us to draw some important conclusions. First, the grating can produce appreciable diffraction only if the grating interval is comparable to an optical wavelength, i.e. d ~ l ~ 10-4 cm.

You can see how the diffraction pattern will be changed by varying d and l on the screen. The second conclusion, which follows from the equation, is that the positions of principal maxima of the diffraction pattern depend on the wavelength of the incident radiation.