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I am not able to understand what are Fresnel bi-Prism andMichelson Inteferometer so help me out!
Q1)Explain Fresnel bi-Prism using the images above. Includeintroduction, relevant equation/formulas , explanations,main points and conclusion in the answer.(Mark:10) Q2)Explain MichelsonInteferometer using the images above. Includeintroduction, relevant equation/formulas , explanations,main points and conclusion in the answer. (Mark:10)
13.5 FRESNEL'S BIPRISM* Soon after the double-slit experiment was performed by Young, the objection was raised that the bright fringes he observed were probably due to some complicated modification of the light by the edges of the slits and not to true interference. Thus the wave theory of light was still questioned. Not many years passed, however, before Fresnel brought forward several new experiments in which the interference of two beams of light was proved in a manner not open to the above objection. One of these, the Fresnel biprism experiment, will be described in some detail. A schematic diagram of the biprism experiment is shown in Fig. 131. The thin double prism P refracts the light from the slit sources S into two overlapping beams ac and be. If screens M and N are placed as shown in the figure, interference fringes are observed only in the region bc. When the screen ae is replaced by a photographic plate, a picture like the upper one in Fig. 13J is obtained. The closely spaced fringes in the center of the photograph are due to interference, while the wide fringes at the edge of the pattern are due to diffraction. These wider bands are produced by the vertices of the two prisms, each of which acts as a straightedge, giving a pattern which will be discussed in detail in Chap. 18. When the screens M and N are removed from
T I S₁ d S 12 S₂ -B- P M 0 FIGURE 131 Diagram of Fresnel's biprism experiment. the light path, the two beams will overlap over the whole region ae. The lower photo- graph in Fig. 13J shows for this case the equally spaced interference fringes super- imposed on the diffraction pattern of a wide aperture. (For the diffraction pattern above, without the interference fringes, see lowest figures in Fig. 18U.) With such an experiment Fresnel was able to produce interference without relying upon diffraction to bring the interfering beams together. b Just as in Young's double-slit experiment, the wavelength of light can be deter- mined from measurements of the interference fringes produced by the biprism. Calling B and C the distances of the source and screen, respectively, from the prism P, d the distance between the virtual images S₁ and S₂, and Ax the distance between the suc- cessive fringes on the screen, the wavelength of the light is given from Eq. (13d) as (13f) 2 Ax d B + C
Thus the virtual images S₁ and S₂ act like the two slit sources in Young's experiment. In order to find d, the linear separation of the virtual sources, one can measure their angular separation on a spectrometer and assume, to sufficient accuracy, that d=B0. If the parallel light from the collimator covers both halves of the biprism, two images of the slit are produced and the angle between these is easily measured with the telescope. An even simpler measurement of this angle can be made by holding the prism close to one eye and viewing a round frosted light bulb. At a certain distance from the light the two images can be brought to the point where their inner edges just touch. The diameter of the bulb divided by the distance from the bulb to the prism then gives directly. Fresnel biprisms are easily made from a small piece of glass, such as half a microscope slide, by beveling about to in. on one side. This requires very little grinding with ordinary abrasive materials and polishing with rouge, since the angle required is only about 1º. 8 FUNDAMENTALS OF OPTICS FIGURE 13J Interference and diffraction fringes produced in the Fresnel biprism experiment.
13.8 DIVISION OF AMPLITUDE. MICHELSON† INTERFEROMETER Interference apparatus may be conveniently divided into two main classes, those based on division of wave front and those based on division of amplitude. The previous examples all belong to the former class, in which the wave front is divided laterally into segments by mirrors or diaphragms. It is also possible to divide a wave by partial reflection, the two resulting wave fronts maintaining the original width but having reduced amplitudes. The Michelson interferometer is an important example of this second class. Here the two beams obtained by amplitude division are sent in quite different directions against plane mirrors, whence they are brought together again to form interference fringes. The arrangement is shown schematically in Fig. 13N. The main optical parts consist of two highly polished plane mirrors M₁ and M₂ and two plane-parallel plates of glass G₁ and G₂. Sometimes the rear side of the plate G₁ is lightly silvered (shown by the heavy line in the figure) so that the light coming from the source S is divided into (1) a reflected and (2) a transmitted beam of equal intensity. The light reflected normally from mirror M₁ passes through G₁ a third time and reaches the eye as shown. The light reflected from the mirror M₂ passes back through G₂ for the second time, is reflected from the surface of G₁ and into the
FIGURE 13N Diagram of the Michelson interfer- ometer. TV, -M₁ (1) 4/E G₁ G₂ E (2) M₂ eye. The purpose of the plate G₂, called the compensating plate, is to render the path in glass of the two rays equal. This is not essential for producing fringes in mono- chromatic light, but it is indispensable when white light is used (Sec. 13.11). The mirror M₁ is mounted on a carriage C and can be moved along the well-machined ways or tracks T. This slow and accurately controlled motion is accomplished by means of the screw V, which is calibrated to show the exact distance the mirror has been moved. To obtain fringes, the mirrors M₁ and M₂ are made exactly perpendicular to each other by means of screws shown on mirror M₂.
Even when the above adjustments have been made, fringes will not be seen unless two important requirements are fulfilled. First, the light must originate from an extended source. A point source or a slit source, as used in the methods previously described, will not produce the desired system of fringes in this case. The reason for this will appear when we consider the origin of the fringes. Second, the light must in general be monochromatic, or nearly so. Especially is this true if the distances of M₁ and M₂ from G₁ are appreciably different. An extended source suitable for use with a Michelson interferometer may be obtained in any one of several ways. A sodium flame or a mercury arc, if large enough, may be used without the screen L shown in Fig. 13N. If the source is small, a ground-glass screen or a lens at L will extend the field of view. Looking at the mirror M₁ through the plate G₁, one then sees the whole mirror filled with light. In order to obtain the fringes, the next step is to measure the distances of M₁ and M₂ to the back surface of G₁ roughly with a millimeter scale and to move M₁ until they are the same to within a few millimeters. The mirror M₂ is now adjusted to be perpendicular to M₁ by observing the images of a common pin, or any sharp point, placed between the source and G₁. Two pairs of images will be seen, one coming from reflection at the front surface of G₁ and the other from reflection at its back surface. When the tilting screws on M₂ are turned until one pair of images falls exactly on the other, the interference fringes should appear. When they first appear, the fringes will not be clear unless the eye is focused on or near the back mirror M₁, so the observer should look constantly at this mirror while searching for the fringes.
P' 2d P" I 2dcos L₁ La M₁ M₂ Idd 2d- FIGURE 130 Formation of circular fringes in the Michelson interferometer. When they have been found, the adjusting screws should be turned in such a way as to continually increase the width of the fringes, and finally a set of concentric circular fringes will be obtained. M₂ is then exactly perpendicular to M₁ if the latter is at an angle of 45° with G₁.