Match the following lists :List – I List – II a. \(\pi a\,NA/\lambda\) i. attenuation factor (dB/km) b. \(10\log_{10}\left(\dfrac{P_{in}}{P_{out}}\right)\) ii. Intermodal time delay c. \(\dfrac{l}{L}\dfrac{dt_g}{d\lambda}\) iii. Dispersion causing pulse spreading d. \(\dfrac{L(n_1-n_2)n_1}{n_2c}\) iv. Number of modes produced by an optical fibre
a-iv, b-i, c-iii, d-ii
Identify each expression by what it is built from.
b → i, attenuation. This is the easiest and it fixes the table. A ratio of input to output power in decibels is the definition of loss:
\(\alpha=\dfrac{10}{L}\log_{10}\dfrac{P_{in}}{P_{out}} \ \ \text{dB/km}\)
a → iv, number of modes. The combination \(\dfrac{\pi a\,NA}{\lambda}\) is the fibre's normalised frequency — the V-number — written with the radius a, the numerical aperture NA and the wavelength. It is dimensionless, which is the giveaway, and the mode count follows from it:
\(V=\dfrac{2\pi a}{\lambda}\,NA, \qquad M\approx\dfrac{V^{2}}{2}\ \ \text{(step index)}\)
A fibre is single-mode when V < 2.405, the first zero of the Bessel function J0 — which is why single-mode fibre needs a core only a few micrometres across.
c → iii, dispersion. The expression is a derivative of group delay with respect to wavelength, normalised to length. That is precisely the definition of the dispersion coefficient, usually quoted in ps/(nm·km); multiplied by the source spectral width it gives the pulse spreading.
d → ii, intermodal delay. Only refractive indices, a length and the velocity of light appear, so the result is a time. It is the classic step-index result for the delay between the fastest ray (axial) and the slowest (at the critical angle):
\(\Delta t=\dfrac{L\,n_1(n_1-n_2)}{n_2 c}=\dfrac{Ln_1\Delta}{c}\)
Assemble. a-iv, b-i, c-iii, d-ii — option 3.
The dimensional shortcut. One expression is dimensionless (a mode count), one is in decibels (a loss), one is a derivative with respect to wavelength (a dispersion) and one has the dimensions of time (a delay). Matching by dimensions alone answers the question without recalling a single fibre formula.
Why intermodal delay matters. It is the dominant limit on step-index multimode fibre, and it is what graded-index profiles were invented to cancel — the outer rays travel a longer path but through a lower-index region, so all modes arrive together.
Hence, the correct matching is a-iv, b-i, c-iii, d-ii.
Similar Questions
If 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
Which of the following is not a usual classification of optical fibre ?
Assertion (A) : In the propagation of light along multimode graded index fibre, the rays moving toward the cladding travel longer path with greater velocity than the rays travelling shorter path near the axis of fibres. These cause less spreading as compared to spreading caused by multimode step index fibre.
Reason (R) : The velocity varies because refractive index of the multimode graded index fibre increases with radial distance from the centre (axis).
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?
Assertion (A) : Attenuation and dispersion have negative effects on the propagation of signal in the optical fibres.
Reason (R) : Optical signal degradation is caused due to structural imperfections of the fibre material.
Select your answer using the codes given below.
A fiber has a core radius of 6 μm, operating wavelength = 1550 nm. The V-number of the fiber is given by :
In linearly polarized modes traversing in the optical fibers the LP01 is exactly equal to :
The value of Numerical Aperture in case of optical fiber is
The core of an optical fiber has
The core diameter of single mode fiber is in the order of
Important Questions from Optical Fiber
The material used for making optic-fibre cable in general is-
Multimode step-index fiber with a core diameter of 80 μm and a relative index difference of 1.5% is operating at a wavelength of 0.85 μm. If the core refractive index is 1.48, then the normalized frequency for the fiber is
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:
In optical fibers, the Rayleigh scattering is proportional to:
A graded indexed optical fiber has a parabolic refractive index profile (α = 2). If the fiber has a numerical aperture = 0.22 the total number of guided modes at a wavelength of 1310 nm is given by:
