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Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n_(1) surrounded by a medium of lower refractive index n_(2) . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n_(1) and n_(2) as shown in the figure . all rays with the angle of incidence i less than a particular value of i_(m) are confined in the medium of refractive index n_(1) . The numerical aperture (NA) of the structure is defined as "sin"i_(m) For two structures namely S_(1) with n_(1) = sqrt(45) //4 "and" n_(2) = 3//2 , "and" S_(2) with n_(1) = 8//5 "and" n_(2) = 7//5 and taking the refractive index of water to be 4/3 and that of air to be 1 , the correct option (s) is (are) |
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Answer» NA of `S_(1)` IMMERSED in water is the same as that of `S_(2)` immersed in liquid of REFRACTIVE index `(4)/(sqrt(5))` nsini = `n_(1) "sin"(90- theta)` ` " n sini" = n_(1) "cos" theta …..(i)` Here for `i_(m) , theta = C "and " "sin" C = (n_(2))/(n_(1))` fromeq. (i) , `n"sin"i_(m)= n_(1) sqrt((1 - n_(0)^(2))/(n_(1)^(2))) = sqrt(n_(1)^(2) - n_(2)^(2))` `implies "sin"i_(m) = sqrt(n_(1)^(2) - n_(2)^(2))/(n)` Now , for (A) `(NA)_(s_(1)) = (3)/(4)sqrt((45)/(16) - (9)/(4)) = (3)/(4) xx (3)/(4) = (9)/(16)` `(NA)_(s_(2)) = (3sqrt(15))/(16) sqrt(64)/(25) - (49)/(25)) = (3sqrt(15))/(16) (1)/(5)sqrt(15) = (9)/(16)` For (B) `(NA)_(s_(1)) = sqrt(15)/(6) xx (3)/(4) = sqrt((15))/(8)` `(NA)_(s_(2)) = (3)/(4) = sqrt(15)/(5)` Not equal For (C) `""(NA)_(s_(1)) = 1 xx (3)/(4) = (3)/(4)` `(NA)_(s_(2)) = sqrt(15)/(4) xx sqrt((15))/(5) = (15)/(4 xx 5) = (3)/(4)` For (D) `""(NA)_(s_(1)) = (3)/(4)` `(NA)_(s_(2)) = (3)/(4) sqrt(15)/(5)` Not equal |
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