 Namaste. Myself, Dr. Mrs. Preeti Sunil Joshi, Assistant Professor, Department of Humanities and Sciences from Walsham Institute of Technology, Solapur. In the previous session, we have seen that what is diffraction and types of diffraction. By the end of this session, student will be able to learn about diffraction grating and its theory. The contents include diffraction grating and theory of diffraction grating. Before starting the session, let us memorize some basic terms that is what is diffraction. Diffraction is the bending of waves around an obstacle and deviation from a rectilinear path. There are two types of diffraction. In Fresnel diffraction, the source and screen are effectively at finite distances from the obstacle and in Fraunhofer diffraction, the source of light and the screen are effectively at infinite distances from the obstacle. We have seen these differences in detail in previous session. Let us now understand what is plane diffraction grating and how it is prepared. A diffraction grating consists of a very large number of narrow slits. These slits are separated by opaque surfaces. When the light wave front is incident on a grating surface, then the light is transmitted through the slits and obstructed by the opaque portions. The gratings are prepared by ruling equidistant parallel lines on a large glass surface. These lines are drawn with a fine diamond point. The space in between any two lines is transparent to light and the line portion is opaque to light. When white light enters the grating, the light components are diffracted at angles that are determined by the respective wavelengths. Picking out diffracted light makes it possible to select the required light component. In short, for parallel beams that enter neighbouring slits, as shown in the figure, the light is reinforced when the light path difference is a multiple of wavelength. The light from all the slits is reinforced in the same way to produce diffracted light. A diffraction grating may work either in reflection or transmission as shown here. Now what is the difference between reflective and transmission grating? In a transmission grating, the diffracted light is passed through at an angle equal to the diffraction angle and for reflective gratings, the light is first diffracted by the grating and then reflected by the coating at an angle equal to the diffraction angle. Both reflective and transmission gratings follow the diffraction grating equation. These are the images of plane diffraction grating which you might have seen in the laboratory while performing the experiment. When there are tremendous number of slits, typically about 60,000, the slits form what is called a diffraction grating. The slits can be the spaces between very fine equally spaced opaque lines on a piece of glass. The lines are ruled with 3 inches. The lines are ruled with high precision. The 60,000 or so lines on a grating only about 3 inches wide. The spectra which can be obtained with these gratings are far more precise than the spectra from prisms. So diffraction gratings are often used instead of prisms in spectroscope. Gratings are ruled from 70 lines per millimeter for infrared work to 1800 lines per millimeter that is for ultraviolet work. Now we will see the theory that is related with the diffraction grating. Consider a plane diffraction grating held normal to the plane of the page as shown in figure and represented by the section A, B, C up to G. Let the width of the transparent portion AB is equal to A and opaque portion BC be equal to B. The distance A plus B is equal to D and that is called the grating constant or which is also known as grating period. Let a beam parallel beam of wavelength lambda be incident normally on the grating surface. Then all the secondary waves travelling in the same direction as that of the incident light will come to focus at point P on the screen which is placed at the focal plane of collecting lens L. Now this point P0 gives the position of central bright maximum. Let us consider the secondary waves travelling in a direction inclined at an angle theta with the direction of the incident light as shown in the figure. The waves travel different distances and it is obvious that there is a path difference between the waves coming out from each slit and bending at an angle theta. These secondary waves come to focus at point P1 on the screen. The intensity at P1 will depend on the path difference between the secondary waves originating from the respective points A and C of the two neighbouring slits. In figure we can see that AB is equal to small a and BC is equal to small b. The path difference between the secondary waves starting from A and C is equal to AC sin theta. Now this point P1 will be the maximum intensity if the path difference is equal to the integral multiple of wavelength. If A plus B sin theta is equal to lambda we obtain maximum intensity at P1. When A plus B sin theta is equal to 2 lambda there will be again a maximum and so on. There will be minimum intensity in between central maximum P0 and first maximum and so on. Similar maximum and minima are obtained on the other side of the central maximum. Thus on each side of the central maximum P1 principal maxima and minimum intensity are observed due to diffracted light. So the formula is A plus B sin theta is equal to n lambda where A plus B is called the grating constant or grating element. When the number of lines are given per centimeter then A plus B can be calculated by 1 divided by number of lines per centimeter and when the number of lines are given per inch then the formula will be A plus B is equal to 2.54 divided by number of lines. Now pause the video and try to solve this numerical. Check for the correct answers, desire the references, thank you.