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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 \( \mathbf{n}_{1} \) surrounded by a medium of lower refractive index \( \mathbf{n}_{2} \). 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 \( i_{\mathrm{m}} \) are confined in the medium of refractive index \( \mathrm{n}_{1} \). The numerical aperture (NA) of the structure is defined as \( \sin i_{\mathrm{m}} \)
- 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)
(A) NA of \( S_{1} \) immersed in water is the same as that of \( S_{2} \) immersed in a liquid of refractive index \( \frac{16}{3 \sqrt{15}} \)
_ (B) NA of \( S_{1} \) immersed in liquid of refractive index \( \frac{6}{\sqrt{15}} \) is the same as that of \( S_{2} \) immersed in water.
- (C) NA of \( S_{1} \) placed in air is the same as that of \( S_{2} \) immersed in liquid of refractive index \( \frac{4}{\sqrt{15}} \).
- (D) NA of S. placed in air is the same as that of S. vlaced in water.
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