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.
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