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Lens Maker's Formula

Light guidanc...

Question

Light guidance in an optical fibre 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 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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Similar questions

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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}

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

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sin i_{m}

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_{1}

N A_{2} (N A_{2} < N A_{1})

are joined longitudinally, the numerical aperture of the combined structure is

Q. Light guidance in an optical fibre can be understood by considering a structure comprising of thin solid glass cylinder of refractive index

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surrounded by a medium of lower refractive index

n_{2}

.
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n_{1}

n_{2}

as shown in the figure. All rays with the angle of incidence

i

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are confined in the medium of refractive index

n_{1}

. The numerical aperture (NA) of the structure is defined as

sin i_{m}

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