JEE Advanced · 2015 · 24 May 2015 · Paper 2 · Geometrical Optics

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PARAGRAPH 2

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}

(

N A_{2} < N A_{1}

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

(A) $\frac{N A _{1} N A _{2}}{N A _{1} + N A _{2}}$
(B) $N A_{1} + N A_{2}$
(C) $N A_{1}$
(D) $N A_{2}$ ✓ Correct

Answer: (D)

Solution

When two optical fibers with different numerical apertures are joined longitudinally, the combined system's numerical aperture is limited by the fiber with the smaller NA.

The numerical aperture determines the acceptance cone angle for light entering the fiber. Light that can enter the first fiber (with

N A_{1}

) but exceeds the acceptance angle of the second fiber (with

N A_{2} < N A_{1}

) will not propagate through the combined structure.

Therefore, the effective numerical aperture of the combined structure is the smaller of the two:

N A_{2}

.

The answer is (D).

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JEE Advanced · 2015 · 24 May 2015 · Paper 2 · Geometrical Optics

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