![]() Very close to that predicted by Equation (17). The minimum of each graph did in fact take place at a value of Goes to a minimum by watching the diffracted beams, as both In this case it was difficult to find the value of Therefore the minimum angle reached between any two adjacent diffraction lines is the same.Ĭalculated from Equations (17) and (18), respectively. Satisfies Equation (17), the angle between diffraction lines of order n and It can easily be verified that when this condition is met, Then differentiation of this equation with respect to ) at which the angle of deviation becomes a minimum, Calculated and measured values of the rotation angle of the grating ( ![]() To see this, we write Equation (3) for n and again for As a result, the angle between any two adjacent diffracted rays decreases first and then increases as the grating turns, resulting in a minimum value. As can be seen from Table 1, the agreement between the measured values and the calculated values is excellent.Īnother interesting feature of these diffraction patterns is that the angle through which the grating has to turn for a diffraction line to go to its minimum deviation increases with the order of diffraction n. The standard deviations of the theoretical values are calculated using propagation of errors and the standard deviation in d. Each measured value reported in the table is the average of ten runs along with its standard deviation. Table 1 shows the results of our measurements and their comparison with the calculated values. The line distance of the grating was obtained by measuring it at ten different points of the grating, using the laser light. In order to test these results, we used a diffraction grating with a line distance of There are no other minima or maxima in the angle of deviation. The minimum angle of deviation for the nth-order diffraction is then given by Relative to the normal incidence, given by The minimum angle of deviation for the nth-order diffracted beam takes place when the grating rotates through an angle It is easily verified that under this condition, Then adding the first of Equations (9) and (10) gives Furthermore, substituting the above equation into Equation (2), we obtain Therefore, the possibility of a minimum or maximum in Equation (3) exist only if one of the following conditions is satisfied: ), corresponding to a clockwise rotation. We shall only consider counterclockwise rotations of the diffraction grating ( We are, however, interested in the higher-order diffractions and the behavior of The diffraction grating is rotated (a) counterclockwise ( A diagram showing the angle of deviationīetween a diffracted ray of light and the incident ray. ![]() Is negative if the grating turns counterclockwise ( Figure 2(a)) and positive if the grating turns clockwise ( Figure 2(b)).įigure 2. Obviously, in terms of the deviation angle Is positive if measured counterclockwise from the direction of incident light and negative if measured clockwise. However, instead of the diffraction angleīetween a diffracted beam and the incident beam, as shown in Figure 2. Now suppose that we illuminate a diffraction grating by a monochromatic ray of light of wavelengthĪnd then turn the grating, keeping the direction of the incident light fixed, starting from normal incidence, the angle through which the grating turns would become the angle of incidence for light, which is Is the angle of nth-order diffraction, andĪre considered positive if measured counterclockwise from the axis (normal to the diffraction grating) and negative if measured clockwise, as shown in Figure 1. , the general equation for the condition of constructive interference is given by When a diffraction grating of line distance d is exposed to a light ray of wavelength In this article, we study the general behavior of various diffracted lines as a result of rotation of the diffraction grating. Rotating all-glass diffraction gratings can be used as beam splitting frequency shifter in laser Doppler anemometers. The Doppler frequency shift in various diffraction orders produced as a result of a rotating radial diffraction grating can be used for optical modulation. For example, a pair of counter rotating diffraction gratings can be used in laser beam scanners for obtaining a linear scan rate for a flat field recorder. Rotating diffraction gratings have a number of applications.
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