Diffraction by single slit

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Information about Diffraction by single slit

Published on September 11, 2008

Author: Abhishekgor90

Source: authorstream.com

Diffraction by single slit : Diffraction by single slit -Abhishek A Gor(248) Diffraction : Diffraction When waves encounter obstacles, the bending of waves around the edges of an obstacle is called “DIFFRACTION”. DIFFRACTION : DIFFRACTION S S A B FIG 1.1 Slide 4: Here we have a source s emitting waves having plane wavefronts. As the wavefronts pass through the slit ab,they are diffracted and are able to reach even those regions behind ab which they would be unable to reach had the rays not bended. One more thing to be noted here is that the shape of the wavefronts change as they pass through the slit. The reason for this bending can be explained with the help of huygens principle. Slide 6: Diffraction by single slit,& its pattern. Slide 7: Huygen’s principle:-each particle lying on any wavefront acts as an independent secondary source and emits from itself secondary spherical waves.After a very small time interval, the surface tangential to all these spherical wavelets,gives the position and shape of the new wavefront. It will be more clear from the following example of plane wavefronts. Let p1,p2,p3,…pn be points very close to each other and equidistant from each other on the plane incident wavefront. Slide 8: To obtain the new wavefront we consider p1,p2,..Pn as independent sources and circular arcs with same radius from each of these points. Now the plane a’ tangential to all these imaginary surfaces gives the new wavefront. We move on to using huygen’s principle for explanation of diffraction. Consider figure 1.1 A A’ P1 P2 P3 P4 PN Slide 9: The dimensions of the slit are finite.As a result,applying huygen’s principle we can say that the new wavefront obtained will be something like the surface shown in figure. Slide 10: Types of diffraction There are two types of diffraction. 1)Fresnal diffraction 2)fraunhoffer diffraction Slide 11: Fresnel diffraction Fraunhofer diffraction FRESNAL DIFFRACTION : FRESNAL DIFFRACTION When the distance between the slit ab and source of light s as well as between slit ab and the screen is finite, the diffraction is called Fresnal diffraction. In Fresnal diffraction the waves are either spherical or cylindrical. FRAUNHOFER DIFFRACTION : FRAUNHOFER DIFFRACTION If light incident on slit ab is coming from infinite distance, the distance between obstacle a and screen c is infinite, the diffraction is called Fraunhofer diffraction. In Fraunhofer diffraction the incident waves should have plane wavefronts. Slide 14: 2. Fraunhofer diffraction by single silt L1 L2 A E Slide 15: LET THE WIDTH OF THE SLIT BE ‘d’. Here the wavefronts are plane as the rays are parallel. When these rays are incident on the slit, then according to huygen’s principle all points on the slit act as secondary sources having same phase. Point p0 lying on the screen is on the perpendicular bisector of slit ab. All the waves passing through slit ab are converged to the point p0 by the lens l. Now all these rays have traveled the same distance in the same medium and hence we can say that when they reach p0,they will have the same phase and as a result produce a bright fringe at the center. Slide 16: NOW CONSIDER THE RAYS DIFFRACTED AN ANGLE q WITH RESPECT TO THE CENTRAL LINE. These rays get superposed at point p1 of the screen with the help of the lens. Draw am perpendicular to BL.As X IS THE MIDPOINT OF THE SLIT BX=AX=d/2. The optical path of all rays reaching p1 from am is the same, and hence only the path difference corresponding to the remaining part is to be considered. We intend to find the values of q which correspond to the dark spot on the screen. Let the value of q be such that XY= l/2. At p1 the path difference between rays being l/2,destructive interference will occur among them. Slide 17: Just as the pair of a and X, we may get points on XB corresponding to points on ax such that, the rays emitted from these points may produce destructive interference at point p1. Thus p1 becomes a dark point. On the other side of p0 at the symmetric point p1’ dark spot is produced. Now BAM= q. So sinq=XY/AX= l/2/d/2. So sinq=l/d. Slide 18: Now we’ll find out the condition for bright spot. In the figure the rays are diffracted at an angle q’ with respect to x1p0 and focused at p2 with the help of lens l. Draw am perpendicular to BL.The path difference between rays emerging from a and x superposing at p2 is XY. Suppose q’ is such that XY= l/2. So X'Y'’=l and BM=3 l/2. As explained earlier rays emerging from ax and xx’ will interfere destructively at p2 and their effect is cancelled. Now the rays emerging from X'B is not nullified. Thus some intensity is obtained at p2 due to rays emerging from X'B. Slide 19: NOW XAY= q’. Sin q’=XY/AX. Sin q’=3l/2d. The above equation is the condition for the first bright spot on the screen. Slide 20: In general the condition for the mth order minimum can be written as :- sinqm=ml/2d. Similarly for mth order maximum:- sinqm=(2m+1)l/2d Slide 21: The graph for the values of intensity v against corresponding values of q is as shown below: q I Slide 22: To determine the wave length of monochromatic lens we can use the diffraction at single slit. To understand this let’s understand Schuster’s method. Slide 23: A spectrometer is basically an instrument for observing spectra and measuring angles of deviation of light by a prism. The essential parts of a spectrometer, shown in figures . (a) a collimator This is a tube with an adjustable slit at one end and an achromatic converging lens system at the other. The slit should be vertical, and it is usually placed at the focus of the lens so that when it is illuminated a beam of parallel light emerges from the collimator. The collimator is fixed to the base of the instrument. Slide 24: (b) a prism table This should be horizontal and can be rotated about a vertical axis. A vernier scale allows the rotation to be measured with respect to the collimator (not used in this experiment). Note that 1 degree = 60 minutes of arc. (c) a telescope This is mounted so that it is free to rotate about the same axis as the prism table. It may be focused to receive parallel light from the collimator. The rotation of the telescope can be measured by another vernier scale. There are cross-wires in the eyepiece of the telescope and these should be vertical and horizontal. Slide 26: Focusing the spectrometer · Rotate the telescope to view a point within the laboratory as distant as is convenient. · focus the telescope to give a sharp image. · Now focus the cross-wires by adjusting the eyepiece of the telescope until the cross-wires appear sharp. The cross-wires should be horizontal and vertical. The eyepiece should not be touched after this adjustment has been made. Slide 27: · Place the prism on the prism table with the ground glass face next to the support bracket. · Place a filament lamp at the slit. · Set the instrument so that white light (from the filament lamp) from the collimator falls on the face AC as shown. Slide 28: the telescope until the image is seen. You will observe a continuous spectrum, the red light being least deviated. The beam will be refracted at surface AC and at surface AB. The angle between the incident and the emergent direction of the light through the prism is called the angle of deviation, d [see figure]. · Replace the filament lamp with the mercury lamp. A line spectrum will now be observed. Make the slit width as narrow as practicable. · Rotate the prism table clockwise and anticlockwise without losing the spectrum viewed through the telescope. · Observe that the deviation of some particular colour should decrease, reach a minimum and then increase, i.e. there is a minimum deviation. Slide 29: Schuster's Method - to focus the telescope and collimator Now you are ready to focus the collimator and the telescope. · View the spectrum from the helium lamp through the telescope, and turn the prism to the angle for minimum deviation. Turn the prism table away by about 5 degrees from the minimum deviation position so that the ground glass face of the prism is more nearly parallel to the axis of the collimator. Focus the collimator. Slide 30: . Place the lamp at the slit. . With the prism removed from the prism table view the image of the slit through the telescope in the straight-through position, [see figure]. So the rays entering and leaving the prism are parallel. Adjust the width of slit till you get a clear diffraction pattern. Then take readings of the telescope position on the pair of diametric vernier scales attached to the telescope. It is important that you read both vernier scales for each setting. Observation Table:- : Observation Table:- Slide 33: Where, b= width of slit n=Order of dark band θ=Angle of the dark band Thus, We can find the wave length by λ=bsinθ equation. n Diffraction by single slit : Diffraction by single slit -Abhishek A Gor(248)

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