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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 \( i_{m} \) are confined in the medium of refractive index \( n_{1} \). The numerical aperture (NA) of the structure is defined as \( \sin i_{m} \).
If two structures of same cross-sectional area, but different numerical apertures \( N A_{1} \) and \( N A_{2}\left(N A_{2}N A_{1}\right) \) are joined longitudinally, the numerical aperture of the combined structure is
(1) \( \frac{N A_{1} N A_{2}}{N A_{1}+N A_{2}} \)
(2) \( N A_{1}+N A_{2} \)
(3) \( N A_{1} \)
(4) \( N A_{2} \)
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