A fiber has a core radius of 6 μm, operating wavelength = 1550 nm. The V-number of the fiber is given by :
4.104
This question was cancelled by UGC. The official answer key records code 9 against it, meaning every option was credited and all candidates were awarded the two marks whatever they marked. The discussion below therefore gives the best-supported reading of the item rather than a uniquely correct option.
The V-number, or normalised frequency.
\(V=\dfrac{2\pi a}{\lambda}\,NA=\dfrac{2\pi a}{\lambda}\sqrt{n_1^{2}-n_2^{2}}\)
It is dimensionless, and it is the single parameter that decides how many modes a step-index fibre supports.
Note what the question does not give. The numerical aperture — or equivalently the core and cladding indices — is not stated, so V cannot be computed from the printed data alone. The question as reproduced is incomplete, and the missing quantity has to be recovered from the answer.
Step 1 — evaluate the geometric factor.
\(\dfrac{2\pi a}{\lambda}=\dfrac{2\pi\times6\times10^{-6}}{1550\times10^{-9}}=\dfrac{37.70}{1.55}=24.32\)
Step 2 — work backwards from each option.
| V | Required NA = V/24.32 |
|---|---|
| 2.756 | 0.113 |
| 2.956 | 0.122 |
| 4.104 | 0.1688 |
| 2.329 | 0.096 |
Step 3 — identify which NA comes from standard source data. Using the usual form \(NA=n_1\sqrt{2\Delta}\) with the textbook pair \(n_1=1.48\) and a relative index difference \(\Delta=0.65\%\):
\(NA=1.48\sqrt{2\times0.0065}=1.48\times0.1140=0.1688\)
\(V=24.32\times0.1688=4.104\)
an exact match, and the only option that corresponds to a round, standard set of fibre parameters. So option 3 is the intended answer.
What the value means. The single-mode condition is
\(V \lt 2.405\)
the first zero of the Bessel function J0. With V = 4.104 this fibre is multimode, supporting roughly
\(M\approx\dfrac{V^{2}}{2}\approx8\ \text{modes}\)
which is consistent with the unusually large 6 μm core radius — genuine single-mode fibre at 1550 nm has a core radius of about 4.1 μm, not 6.
The design lever. Since V falls as either a or NA is reduced, single-mode operation is bought with a very small core and a very small index difference — which is precisely why single-mode fibre is harder to splice and to couple light into than multimode.
Hence, the V-number is 4.104.
Similar Questions
The core of an optical fiber has
The core diameter of single mode fiber is in the order of
Consider the following statements :
Losses in optical fibers are caused by
1. Impurities in the fibre material
2. Microbending
3. Splicing
4. Step index profileOf these statements :
Assertion (A) : Optical fibers have broader bandwidth compared to conventional copper cables.
Reason (R) : Low power LASER beams are considered to be very powerful as compared to high power ordinary light beams.
The following is true for the multimode graded index fiber :
1. The refractive index varies as a function of radial distance from the centre.
2. The refractive index undergoes sudden change at the cladding boundary.
3. It provides better bandwidth and the data rate than the multimode step index.
4. It provides the better bandwidth and data rate than single mode step index.A multimode step-index fibre has glass core (n1 = 1.5) and fused quartz cladding (n2 = 1.46), which one of the following is the value of acceptance angle ?
Following is not the usual classification of an optical fibre :
Which of the following are the cases of signal attenuation ?
1. Splicing
2. Intermodal Delay
3. Scattering
4. Chromatic DispersionIf numerical aperture and fractional refractive index of an optical fibre are 0.22 and 0.012, respectively. The refractive index of core (µ1) and cladding (µ2) will be
An optical fibre has numerical aperture (NA) of 0.3 and refractive index $\eta_2$ of cladding material is 1.6. What is the refractive index of core material?
Important Questions from Optical Fiber
What is the relation between the refractive index of core n1 and cladding n2?
Graded index fiber is used to
In a multimode fiber (step index), number of modes passing at an operating wavelength of 1300 nm are 1000, the refractive index of the core is 1.50 and that of the cladding is 1.48. The value of core diameter is:
Fibre optic power meters have input for attaching fiber optic connector and detector:
An optical fibre cable consists of three parts. One of these is a protective outercoating of the cable. Select that protective outer coating from the given options.
