 Myself, Dr. Mrs. Preeti Sunil Joshi, Assistant Professor, Department of Humanities and Sciences from Valchand Institute of Technology, Solapur. I welcome you in the session of FAE Optics. The learning outcomes of this session are, by the end of this session, student will be able to learn, release criteria of resolution and resolving power of diffraction grating. The contents include release criteria and resolving power of grating. Let us first see the concept, what is resolution? What do you understand by resolution? Please view this image. Can you see any difference between these images? Please discuss, what are the differences? And from this, can you tell now, what is resolution? Yes, when two objects are very close to each other, they appear as one. And it may not be possible for the eye to see them as separate. If the objects are not seen separately, then we say that the details are not resolved by the eye. Can you tell some devices which are having the ability to distinguish such small details of an object? Yes, they are optical or radio telescope, a microscope, a camera or even an eye. Optical instruments are used to assist the eye in resolving the objects or images. And the method that is adopted to see the close objects as separate objects is called resolution. When two objects are very close to each other, they appear as one. And we say that the details are not resolved by the eye. So, the ability of the optical instrument to produce distinctly separate images of the two objects, which are placed very close to each other, is called the resolving power of any optical instrument. Another definition can be the reciprocal of the smallest angle, subtended at the objective of eye to point objects, which can just be distinguished as separate. The theory of optical instruments is based on the laws of geometrical optics and rectilinear propagation of light. But these laws are only approximately true. When a beam of white light from a point object passes through the objective of a telescope, the lens acts like a circular aperture and produces a diffraction pattern instead of a point image. This diffraction pattern is as shown in the diagram and it is known as Aries disc. If there are two close point objects, then what will happen? Yes, two diffraction patterns corresponding to these two point objects are produced and which may overlap on each other and it may be difficult to distinguish them as separate. To obtain the measure of resolving power of an objective lens, Rayleigh suggested a criteria which is known as Rayleigh's criteria. And according to Rayleigh's criteria, the two images may be regarded as separated if the central maximum of one falls on the first minimum of the other. And this is equivalent to the condition that the distance between the centers of the patterns shall be equal to the radius of the central disc. This is known as Rayleigh's limit of resolution. Now let us consider three cases. Now for a well resolved images, the difference in wavelengths is such that their principal maxima are separately visible. There is a distant point of zero intensity in between the two. Hence the two wavelengths are said to be well resolved. When the difference in wavelengths is smaller and such that the central maximum of wavelengths coincides with the first minimum of the other, the curve shows a distinct dip in the middle of the two central maxima. That is, it shows noticeable decrease in the intensity between the two central maxima indicating the presence of two different wavelengths. Thus the two wavelengths can be distinguished from one another and according to Rayleigh they are said to be just resolved. When the difference in wavelengths is so small that the central maxima corresponding to two wavelengths come still closer and the resultant intensity curve in this case is quite smooth without any dip which shows that if there is only one wavelength source although somewhat bigger or stronger hence the two wavelengths are not resolved. So one of the important properties of diffraction grating is its ability to separate spectral lines which have nearly same wavelength. Thus the resolving power of a diffraction grating is the capacity to form separate diffraction maxima of two wavelengths which are very close to each other. If we consider two very close spectral lines of wavelength lambda and lambda plus d lambda then its spectral resolution is given by lambda upon d lambda where lambda is the mean of the wavelength and d lambda is the difference between the wavelengths. Let us see how to calculate the resolving power of a grating. Let a be represents the surface of a plane transmission grating which is having the grating element a plus b and capital N is the total number of slits as shown in the figure. Let a beam of light having two wavelengths lambda and lambda plus d lambda is normally incident on the grating. Here xy is the field of view of the telescope. p1 we can see is the nth primary maximum of the spectral line of wavelength lambda at an angle of diffraction theta n. And let p2 is the nth primary maximum of wavelength lambda plus d lambda at a diffracting angle theta n plus d theta n. Now according to Rayleigh's criteria the two wavelengths will be resolved if the position of p2 corresponds to the first minimum p1 that is the two lines will be resolved if the principal maximum of lambda plus d lambda in a direction theta n plus d theta n falls over the first minimum of lambda in the direction theta n plus d theta n as the direction of the nth primary maximum for a wavelength lambda is given by the equation a plus b sin theta n is equal to n lambda and similarly the direction of nth primary maximum for a wavelength lambda plus d lambda is given by a plus b sin theta n plus d theta n is equal to n into lambda plus d lambda. Now these two lines appear just resolved if the angle of diffraction theta n plus d theta n also corresponds to the direction of the first secondary minimum after the nth primary maximum at p1. And this is possible if the extra path difference is lambda by n where n is the total number of lines on the grating. Therefore by simplifying these equations we can get the final equation for resolving power of grating as lambda by d lambda is equal to n multiplied by capital N. Thus the resolving power of a grating is independent of grating constant and is directly proportional to the order of the spectrum and the total number of lines on the grating surface. Students, now please pause the video and try to solve this numerical. Check for the correct answer. These are the references. Thank you.