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Question

Light guidance in an optical fiber can be understood by considering a structure comprising of thin solid glass cylinder of refractive index n subscript 1 end subscript surrounded by a medium of lower refractive index n subscript 2 end subscript . The light guidance in the structure takes place due to successive total internal reflections at the interface of the media n subscript 1 end subscript and n subscript 2 end subscript as shown in the figure. All rays with the angle of incidence i less than a particular value im are confined in the medium of refractive index n subscript 1 end subscript . The numerical aperture (NA) of the structure is defined as sin im .

For two structures namely S1 with n subscript 1 end subscript equals square root of 45 divided by 4 and n subscript 2 end subscript equals 3 divided by 2 comma and S subscript 2 end subscript text  with  end text n subscript 1 end subscript equals 8 divided by 5 text  and  end text n subscript 2 end subscript equals 7 divided by 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)

  1. NA of S subscript 1 end subscript immersed in water is the same as that of S subscript 2 end subscript immersed in a liquid of refractive index fraction numerator 16 over denominator 3 square root of 15 end fraction    
  2. NA of S subscript 1 end subscript immersed in liquid of refractive index fraction numerator 16 over denominator square root of 15 end fraction is the same as that of 2 immersed in water    
  3. NA of S subscript 1 end subscript placed in air is the same as that of S subscript 2 end subscript immersed in liquid of refractive index fraction numerator 4 over denominator square root of 15 end fraction    
  4. NA of S subscript 1 end subscript placed in air is the same as that of S subscript 2 end subscript placed in water    

The correct answer is: NA of S subscript 1 end subscript immersed in water is the same as that of S subscript 2 end subscript immersed in a liquid of refractive index fraction numerator 16 over denominator 3 square root of 15 end fraction



    table row cell text end text text F end text text o end text text r end text text end text T I R equals theta greater or equal than theta subscript c end subscript equals s i n to the power of negative 1 end exponent invisible function application open parentheses fraction numerator n subscript 2 end subscript over denominator n subscript 1 end subscript end fraction close parentheses end cell row cell rightwards double arrow r equals 90 to the power of ring operator end exponent minus theta rightwards double arrow n open parentheses sin invisible function application i close parentheses equals n subscript t end subscript sin invisible function application r equals n subscript 1 end subscript cos invisible function application theta end cell row cell rightwards double arrow nsin invisible function application i subscript m end subscript equals 2 n subscript 1 end subscript cos invisible function application theta subscript c end subscript equals n subscript L end subscript square root of 1 minus fraction numerator n subscript 2 end subscript superscript 2 end superscript over denominator n subscript 1 end subscript superscript 2 end superscript end fraction end root equals square root of n subscript 1 end subscript superscript 2 end superscript minus n subscript 2 end subscript superscript 2 end superscript end root end cell row cell N A equals s i n invisible function application i subscript m end subscript equals fraction numerator 1 over denominator n end fraction square root of n subscript t end subscript superscript 2 end superscript minus n subscript 2 end subscript superscript 2 end superscript end root text end text text N end text text o end text text w end text text end text text p end text text u end text text t end text text end text text v end text text a end text text l end text text u end text text e end text text s end text text. end text text end text end cell end table

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