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).
(A) is true, but (R) is false.
Assertion — TRUE. This is exactly how a graded-index fibre works. A ray that strays towards the cladding follows a longer, curved path, but it travels that path faster; a ray near the axis takes the short route but goes more slowly. The two effects nearly cancel, so all modes arrive together and pulse spreading is far smaller than in a step-index fibre:
\(\Delta t_{step}\approx\dfrac{n_1L\Delta}{c} \qquad\text{versus}\qquad \Delta t_{graded}\approx\dfrac{n_1L\Delta^{2}}{8c}\)
Since Δ is only a fraction of a per cent, the graded fibre's dispersion is smaller by a factor of tens to hundreds — which is why it supports far higher bandwidth.
Reason — FALSE, by one word. The refractive index of a graded-index fibre decreases with radial distance from the axis, following the near-parabolic profile
\(n(r)=n_1\sqrt{1-2\Delta\left(\dfrac{r}{a}\right)^{\alpha}}\)
with α ≈ 2. The statement says it increases, which is the opposite.
And the sign matters — it is what makes the assertion work. Since \(v=c/n\), a lower index out towards the cladding is precisely what lets the off-axis rays travel faster and catch up. If the index really did increase outward, those rays would be slower and travelling further, so the spreading would be worse than in a step-index fibre, not better. The reason therefore contradicts the very effect the assertion describes.
A further consequence of the falling profile: rays do not zig-zag with sharp reflections at all but follow smooth sinusoidal paths, being continuously refracted back towards the axis — which also reduces the losses associated with repeated boundary reflections.
Hence, (A) is true, but (R) is false.
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 ?
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?
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 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:
