AIM: To determine the grating element of a diffraction grating using laser source of known wavelength. Prepared by: 1. Jagmeet singh Submitted to: 2. Ankur badhan Mr.Rohit verma 3. Vikas inder singh 4. Pankaj kaplish 5. Bharat bhushan Group : b3 (G2,5)
Diffraction Grating When there is a need to separate light of different wavelengths with high resolution, then a diffraction grating is most often the tool of choice. This "super prism" aspect of the diffraction grating leads to application for measuring atomic spectra in both laboratory instruments and telescopes. A large number of parallel, closely spaced slits constitutes a diffraction grating. The condition for maximum intensity is the same as that for the double slit or multiple slits, but with a large number of slits the intensity maximum is very sharp and narrow, providing the high resolution for spectroscopic applications. The peak intensities are also much higher for the grating than for the double slit. When light of a single wavelength, like the 632.8nm red light from a helium-neon laser at left, strikes a diffraction grating it is diffracted to each side in multiple orders. Orders 1 and 2 are shown to each side of the direct beam. Different wavelengths are diffracted at different angles, according to the grating relationship. DIAGRAM ILLUSTRATING CONCEPT OF DIFFRACTION GRATING The condition for maximum intensity is the same as that for a double slit. However, angular separation of the maxima is generally much greater because the slit spacing is so small for a diffraction grating.
FIGURE SHOWING SEPRATION OF LIGHT The diffraction grating is an immensely useful tool for the separation of the spectral lines associated with atomic transitions. It acts as a "super prism", separating the different colors of light much more than the dispersion effect in a prism. The illustration shows the hydrogen spectrum. The hydrogen gas in a thin glass tube is excited by an electrical discharge and the spectrum can be viewed through the grating. DIFFRACTION ORDERS Since light of different wavelengths are diffracted at different angles, each order is drawn out into a spectrum. Each spectrum is composed of monochromatic images of the. incident bundle, with the blue image nearer to the central axis. However if
monochromatic light is incident on the grating, several output beams will be generated. This type of device can be used for the generation of multiple lasers (i.e. a beamsplitter) The number of orders that can be produced by a given grating is limited by the grating constant d because it cannot exceed 90 degrees. The highest order is given by d/λ. Consequently a coarse grating (with large d) produces many orders while a fine grating may produce only one or two. EXAMPLE OF DIFFRACTION GRATING. The tracks of a compact disc act as a diffraction grating, producing a separation of the colors of white light. The nominal track separation on a CD is 1.6 micrometers, corresponding to about 625 tracks per millimeter. This is in the range of ordinary laboratory diffraction gratings. For red light of wavelength 600 nm, this would give a first order diffraction maximum at about 22. While directing the 632.8 nm red beam of a helium-neon laser through a 600 lines/mm diffraction grating, a cloud was formed using liquid nitrogen. You can see the direct beam plus the first and second orders of the diffraction.
Another way to visualize the diffraction is to take a time exposure while sweeping a ground glass through the beams. This "paints in" the beams of the diffracted laser light. DEVELOPMENT MADE IN FIELDS OF DIFFRACTION GRATING The first man-made diffraction grating was made around 1785 by Philadelphia inventor David Rittenhouse, who strung hairs between two finely threaded screws. This was similar to notable German physicist Joseph von Fraunhofer's wire diffraction grating in 1821. LABORATORY APPLICATIONS OF DIFFRACTION GRATING AIM: To determine the grating elements of diffraction grating using laser source of known wavelength. Apparatus: laser source of known wavelength, a diffraction grating screen, optical bench and a meter scale. THEORY: A diffraction grating is extremely useful device to study diffraction..it consist of an optically Plane glass plate on which are ruled a number of equidistant Parallel straight lines.the lines divided glass plate into opacities and transparencies, thickened of which is of the order of wave length of visible light. The region ushered a line is drawn become opaque lecheries the is pace between the two lines is transparent The number of lines in a plane transmission grating is of the order of 6000 lines per cm. Also as the slits of grating lines in a single, plane, so it is called plane diffraction.it is an important device for the study of spectra. Also as the slits of grating lie in a single plane, so it is called plane diffraction grating. In laboratories an actual grating is not used as it is very costly The original darting is usually ruled on a plane of spectrum: metal by a sharp diamond paint fitted to a dividing engine. For ordinary use replicas of grating are obtained by depositing a very thin film of gelatin on it. The film is removed when dry and is posted on optically plane glass plate. Any number of cheap replicas solution on the surface of ruled grating. The solution evaporates leaning a thin strip of collision which is stripped off. It is then mounted on an optically flat glass plate and this constitute the transmission grating. These days the grating are made by holographic technique.
ABC---- H in fig. represents the section of plane transmission grating supposed perpendicular to the plane of paper. Let the width of clear space or transparency be equal to AB= a and that of ruling or opacity be BC=b The distance(a+b) is called grating element.prints like A and C separated by a distance (a+b) called corresponding points. When a parallel beam of monochromatic light is incident normally on the grating it suffers diffraction. AS shown in fig. ABC---H represent the incident plane wave front and AMN---K represents the transmitted wave front after diffraction at the grating through an angle on. There is no path difference between the rays before reaching the plane ABC----H. The only phase change that occur between the various rays is due to difference in paths traversed by the rays from the plane ABC----H to the plane AMN---K. It is clear that the path difference between the rays from two corresponding pts. A and C is N=(a+d) and on The same is true far any two corresponding points the transmitted beam of parallel light after falling on lens L brought to focus at the point P. The point P will be bright or dark according as the rays reinforce or interfere with one another. They would reinforce and give brightness as a maximum If (a+b) sin(theta n)= n (lamda) They would interfere and produce darkness or a minima if A+b(sin theta n)= (2n+1) They would interfere and produce darkness. When n=o, theta (n)=o, this gives the central bright maximum when n=3,(a+b) sin(theta)= and we get the first bright maximum or first order spectrum. For first order spectrum n=1 (a+b) sin(theta)= Similarly far second order spectrum n=2 (a+b) sinq2=2 Thus sinq2=2sinq This relation helps us to verify that the order of spectrum after the first is second as under certain condition. Second order spectrum is missing and we get the third order spectrum after the first. Every point on slit acts as source of secondary wavelets and the resulting diffraction pattern is due to the interference of secondary wavelets from the various slits. by comparison with the problem of double slit,that in the direction an angle theta,we
will observe the interference due to n synchronous source modulated by diffraction pattern of one slit. When the number of slits n is large, the pattern will consist of set of bright fringes corresponding to maxima of interference pattern the corresponding points from two successive slits are separated by path difference (a+b) and the path difference between the secondary wavelets from them in the direction theta is (a+b)sin Thus the maxima will result when (a+b)sin=n where n=0,1,2,3... However the intensities are modulated by the diffraction pattern from the single slit. These are called the principal maxima and are designated the first,second and third etc. order of diffraction grating with N=6 is shown in fig. there will be as many first order principal maxima as the number of wavelengths in the incident wave. If the light is not monochromatic,then each wave length lines rise to its own primary maxima in each order. Hence, each order consist of spectrum The number of lines N per inch are marked on the grating. The value of grating element (a+b) is grating. (a+b) =2.54 cm ------ N Where number of lines grating per inch then (a+b) = I --- N From fig. we see that path difference between two secondary waves originating from corresponding points A and C of two reigniting slits is zero. Let Q = angle of diffraction A =AB = width of transparent part B =BC = width of opaque part Let D =a +b 1 D is called slit width and is equal to sun of width of transparent and opaque part. In ACD, we have CD =SINQ --- AC CD = AC Sin Q= (AB +BC) sin Q CD= d sin Q 2
The point P onscreen will be a secondary maxima, when path difference 1 is integral multiple of wavelength of light. CD= n n=1,2,3----- --- d sin (theta)n =n---3 On 3 is called grating =n and gives the conduction for farmed on of secondary maxima from diffraction grating. Here 1 is replaced by on which simply shows that angle of diffraction is different for different orders. Let there be N slit width in a unit length of diffraction grating. this number n is called grating element. It is related to : d To find relation between N and d we note that one slit width =d distance ;- Number of slit width in unit distance =1 ----- D Grating element = 1 Slit width N = 1 ----- D We can find N by using 3 and 4 N = sin(theta) ------ N lambda It should be noted that diffraction of light waves can be observed only if slit width d is suitably chosen. To find, the limit on value of d,we note that for all values of on, sin(theta)n<i nd D -------- >nd Since maximum value of n is one diffraction to be observed. Hence d min ->! Thus diffraction can be observed only if size of slit is comparable to wavelength of light used. Procedure ;- 1 Switch on the He-Ne laser. 2 Put the grating between the screen and the laser. 3 The orderly images of diffraction pattern will be seen on the screen. 4 Note down the distance between screen and diffraction grating. 5 Find the angle through which the length ray bends by using give farmula. Sin Q = p1 p1 /2 --------------------------------- [ (p1p1)/2 + ( qp.] 2 1/2 ------- 2 6 6 Calculate the no. of lines /cm using formula N = sin(theta)/n lamda
The grating element is gives by (a+b) =1/N Precaution :- 1 Distance should be measured accurately. 2 Plane of diffraction grating should be 1 to the axis of incident. 3 The light should fall on which of grating surface. 4. The grating should be held from the edges and the ruled surface should not be touched. Result :- The grating element of given diffraction grating. Comes out to be 1.66 x 10-4 cm with %error. 1.7%.