 on optical fiber by bending loss here. So, we have seen the previous the transmission characteristics before three videos. So, in which we have seen the details of how the attenuation is been calculated due to the absorptions and the scattering losses here. So, these are the learning outcomes at end of this session students will be able to estimate the losses due to the bending of a optical fiber here. So, up till now what we have seen is the losses due to the absorption in the ultraviolet region and the infrared region and in which we have seen the eccentric and the eccentric losses and the scattering losses in the linear and the non-linear scattering losses here. In the linear we have seen the Rayleigh and the My scattering and we have seen how to calculate the Rayleigh scattering here. And one more thing we have studied is that is the non-linear scattering in which we have seen the stimulated romance scattering as well as the Iberomium scattering here. So, before starting to this lecture, so just recall, so what is the difference between the single mode fiber and the multi mode fiber here? Because while solving this the bending loss for the optical fiber we should know that the difference between the single mode and the multi mode here. So, the single mode is nothing but only the fundamental mode is going to be transmitted from the transmitter to the receiver side and in the multi mode that is one more than one fundamental modes are being transmitted here. So, that is known as the multi mode here. So, for how you can understand that is the core diameter of the single mode is about 2 micrometers to 6 micrometers or 10 micrometers only. For a multi mode the core diameter is that is 25 micrometers, 50 micrometers, 62 micrometers as well as the 125 micrometers means it is a larger in core diameter here. That is why, so we should understand this. So, now we will start with the bending losses that is depending on the radius of the bend there are the two types of bends here that is a micro bend and the micro bending. So, the micro bend as shown in this figure it is the imperfections of the layer as overlapping of the core and plading will be there there is some micro bends will be there. You know that that whenever the light is going to be transmitted into the core. So, it should follow the total internal reaction that light should not get transmitted to the cladding because otherwise the data will be lost here. So, due to the micro bend here the light at the hit at this micro bend will come out from the into the cladding here and the data will be lost here. So, such type of thing is known as the micro bend. If you want to completely remove these losses here then we have to be manufacturing the optical fiber that is the core and cladding should be made once again there. In the micro bend that is we have seen that it is the bend because due to the radius of curvature is larger than the core radius here that is the core diameter here. So, such type of thing is known as the micro bend here. So, as shown in this figure you know that the light is timely inside this core here. So, it is incident here and it comes out to be in the cladding here. So, that is why there is a loss of data here. Some light may pass through it, but all light should follow the total internal reflection here. So, that is a slightly different between the micro bend and the micro bend here now. So, if you want to calculate the bending losses for the multi mode and the single mode then there is a different formula used for that that is RCM that is known as a 3N1 square into lambda that is lambda is the operating wavelength and 4 pi into N1 minus N2 square that is the refractive index difference raise to 3 by 2. And the second one is the critical radius for the curvature that is the RCS that is for the single mode fiber which is given as 20 lambda by N1 upon N2 3 by 2 that is 2.7 into 48 minus 0.996 lambda by lambda c that is the operating wavelength as well as the cutoff wavelength is there and raise to minus 3 here. So, now we will solve one example on the bending losses how we calculate the critical radius for the single mode as well as the multi mode here now. So, as shown in this example there is a step index is given here. Step index is nothing but the core of the step index is uniform refractive index is uniform and the graded index that is not uniform here. So, for example we have taken the two step index fiber and there are two cases that is case A and case B for multi mode fiber the refractive index is 1.5 that is core refractive index means N1 that is 1.5 it is given and the relative refractive index difference is given that is the 3 percent here means they have not given N2 here. So, we have to calculate that and the operating wavelength is 0.82 micrometer and in the second case we have seen that 8 micrometer core diameter that is the single mode fiber with the core refractive index same as and this means N1 is taken as 1.5 and the relative difference refractive index that is the delta which is given as 0.3 percent here and operating wavelength is given as 1.55 micrometer here. So, we have to estimate the critical radius for the curvature which is large bending loss occurs in the both the cases in the large bending losses here. So, for RCM we should know that it is calculated N1 square lambda that is 4 pi N1 square minus N2 square 3 by 2. So, now we will put all these values into this equation and we will see that how much comes to when critical radius for the RCM. So, before that we should know that how to calculate an N2. So, the refractive index of an N2 is calculated in various manner as now they have given the relative refractive index as a 3 percent less and N1 is given as 1.55. So, for that we need to understand how to it is calculated. So, it is calculated that is delta N1 square upon N2 square 2 N1 square here. So, we will substitute all the values 1.5 and N2 square upon 2 into 1.5 square that is 3 percent that is an delta here. So, now if you calculate this it comes to when N1 square 2 delta N1 square here. So, which comes to when 2.5 0 6 into 2.25 that is 2.1 1 5. So, we substitute these values into RCM that is 3 N1 square into lambda 4 pi N1 square 3.2. So, we will substitute 3 into 2.25 percent to 0.82 and this 2 6 that is micrometer 4 pi. If you calculate N1 square minus N2 square it comes to be 0.135 half. So, which comes to be 9 micrometer which comes to be 9. So, for the critical radius for the multi mode comes to be 9 micrometer here. So, we have substituted the values and directly we have solved for this here. So, the case 1 has been solved here it comes to be an RCM comes to be 9 micrometer here. So, now for the case B. So, which is the core refractive index is taken as the same that is 1 and the delta refractive index is 0.3 percent and difference is there and operating well. In the same manner we have to calculate for the N2. So, we need to calculate for this. So, for case B. So, we solve this. So, which comes to be N2.250 into 0.006 into 2.250 which comes to be N2.237. So, now there is one more thing that is the cutoff wavelength has to be calculated that is cutoff wavelength for the single mode fiber that is lambda C which is calculated 2 pi A N12 delta half upon 2.4 because for single mode it should be less than 2.405 A is the refractive means A N1 is the refractive index and A is the core radius. So, that is why it is given as an 8 micrometer core diameter it is given here. So, we will calculate that is it is diameter. So, we have to take as an half into 1.5 refractive index related to is given as 3 percent 0.3 percent which comes to be 0.06 upon 2.45. So, it comes to be 1.24 micrometer. So, this value has to be substituted in the equation in equation of RCS. So, for RCS which is given now we will solve on next page. So, which is given as an R C equals to 20 lambda N1 minus N2 3 by 2 that is 2.748 minus 0.996 lambda upon lambda C we have just now calculated this as 2 minus 3. So, we will substitute this 2 into 1.55 micrometers that is 10 raise to minus 6 here 0.043 half 2.48 minus 0.96 into 1.5 into minus 6 upon 1.24 which is being 34 millimeter. So, this is my for a single more it is 9 micrometer for RCS 34 millimeter here. So, from this example so, we can understand that the critical radius for the curvature for guided modes can be made extremely small that is guided mode for it can be 9 micrometers it can be made and although this may be a conflict with the preferred design and the operational characteristics. So, in this manner we are going to calculate the RCS and RCM here. So, these are my references. Thank you.