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Optical Fiber

If two struct...

Question

If two structures of same cross-sectional area, but different numerical apertures NA $_{1}$ and $N A_{2} (N A_{2} < N A_{1})$ are joined longitudinally, the numerical aperture of the combined structure is

A

\frac{N A_{1} N A_{2}}{N A_{1} + N_{2}}

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B

N A_{1} + N A_{2}

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C

N A_{1}

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D

N A_{2}

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Solution

The correct option is D $N A_{2}$
$N A_{2} < N A_{1}$
$\Rightarrow i_{m 2} < i_{m 1}$
If the combination is placed in any order, Total internal Reflection if satisfied for lower $i_{m}$ , it can be satisfied for any lower angles as well.
$∴$ $N A_{2}$ will be the numerical aperture of the combined structure.

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