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23 A multimode SIF step index fiber supports normalized frequency V=75, having NA-0.3, core refractive index 1p=1.458 operating at 820nm. Find core radius and refra...

Question

23 A multimode SIF step index fiber supports normalized frequency V=75, having NA-0.3, core refractive index 1p=1.458 operating at 820nm. Find core radius and refractive index of cladding and fractional change in refractive index.OF

23 A multimode SIF step index fiber supports normalized frequency V=75, having NA-0.3, core refractive index 1p=1.458 operating at 820nm. Find core radius and refractive index of cladding and fractional change in refractive index. OF



Answers

What is the index of refraction of the core of an optical fiber if the cladding has $n=1.20$ and the critical angle at the core-cladding boundary is $45.0^{\circ} ?$

Belongs to the chapter geometric optics in which we have to calculate the percentage difference between refractive index of core and refractive index of cladding. Okay so refractive index of core and cladding. So the diagram for this question can be drawn this Okay so this is the diagram for the question in which raised incident in from here to here then it is going towards like in this direction. Okay this is the flooding and this is the core. Okay so now from the snail slow at this point we can write that and one signed titled or we can directly right that an air sign alpha max alpha max. That will be equals two and core. My pleasure. Bye sign beta max. Okay and from here we get betamax equals two ac. Sign an air the verb and code molecular signed alpha max. Okay so now critical angle to see it will be equals to 90 degree minus vita mix. So we will get that 90 degree minus are signed an air the verb and core blurb signed alpha max. Okay so this is a critical angle and for the court leading interface we can write that refractive index of cladding. Refractive index of cladding. This will be equals two refractive index of course manipulated by sine theta C. And we have this value of T. To see. So we can write that and court manipulated by sign off 90 degree minus are signed an air never be and core sign alpha max and this bracket and this another bracket. Now We can calculate the percentage difference. So percentage difference it will be equal to 1- and cladding and cladding. The railway and core molecular by 100%. Okay so after substituting values so we will get that one minus arc sign a sign of 90 degree minus arc sine of an air never be and core sign alpha max Bracket. And this bracket molecular by 100%. Okay, so No we can substitute the value. So we will get that percentage difference. It will be 1- sign off 90 degree minus are signed and refractive index of air. It is one and refractive index of the core. It is 1.141 point 48 and sign alpha mixes equals to 14.0 double three degree. And this bracket and this bracket manipulated by 100%. Okay, so from here after solving we will get that percentage difference Percentage difference. It will be equals two 1.35 degree percentage. Okay, so this is the answer for this question. This is the percentage difference between reflective index of court and the refractive index of cladding.

Belongs to the chapter geometric optics in which we have to calculate the percentage difference between refractive index of core and refractive index of cladding. Okay so refractive index of core and cladding. So the diagram for this question can be drawn this Okay so this is the diagram for the question in which raised incident in from here to here then it is going towards like in this direction. Okay this is the flooding and this is the core. Okay so now from the snail slow at this point we can write that and one signed titled or we can directly right that an air sign alpha max alpha max. That will be equals two and core. My pleasure. Bye sign beta max. Okay and from here we get betamax equals two ac. Sign an air the verb and code molecular signed alpha max. Okay so now critical angle to see it will be equals to 90 degree minus vita mix. So we will get that 90 degree minus are signed an air the verb and core blurb signed alpha max. Okay so this is a critical angle and for the court leading interface we can write that refractive index of cladding. Refractive index of cladding. This will be equals two refractive index of course manipulated by sine theta C. And we have this value of T. To see. So we can write that and court manipulated by sign off 90 degree minus are signed an air never be and core sign alpha max and this bracket and this another bracket. Now we can calculate the percentage difference. So percentage difference it will be equal to one minus and cladding and cladding. The railway and core molecular by 100%. Okay so after substituting values so we will get that one minus arc sign a sign of 90 degree minus arc sine of an air never be and core sign alpha max bracket. And this bracket molecular by 100%. Okay, so no we can substitute the value. So we will get that percentage difference. It will be one minus sign off 90 degree minus are signed and refractive index of air. It is one and refractive index of the core. It is 1.141 point 48 and sign alpha mixes equals to 14.0 double three degree. And this bracket and this bracket manipulated by 100%. Okay, so from here after solving we will get that percentage difference percentage difference. It will be equals two 1.35 degree percentage. Okay, so this is the answer for this question. This is the percentage difference between reflective index of court and the refractive index of cladding.

Let us first. Right. The lens maker. Formula One of what if pique was and minus one one of our one minus one over r two. Now we have to find Remember, we have to find DF over f Remember that if you start from long X and if you differentiate it, then you get I wonder what X, which means it is easier to take. I love it. So if I take a longer than then I will have negative long off if equals long enough and minus one thus no enough one over R one minus one over r two. Now, if we take a different shell with respect to F, then we get negative one of our f. So at this point, you're doing difference. Yet with respect to f equals, I don So we have our end minus one In the denominator, we have got bien b f. Thus everything is constant. So from here we can say that DF over f equals de en over one minus end. But generally he's and is greater than equals one. So we should write it as negative and minus one and deal in the upstairs thought, if I want to write it here for the negative one over and minus Juan de en

As we all know that the critical angle of the material is given by sign P to Z. Is equal to end to by anyone. So simply find it further. In terms of animal, I can write the express an edge and one is equal to and to buy sign courtesy. So just putting the value here, I can write one by sign 40.5°, Unsympathetic. It's and I get the value at one 539. So the refractive index of the transparent solid Each and one is equal to one 54 approx. As our final answer for this problem, I hope you understand how I solve this problem. I just used the general formula to calculate the solution.


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