The value of Numerical Aperture in case of optical fiber is
< 1
Numerical aperture is the sine of the acceptance angle, and a sine can never exceed one — so NA < 1, option 2.
\(NA=\sin\theta_{a}=\sqrt{n_{1}^{2}-n_{2}^{2}}\)
The physical reason it is far below one in practice. Guidance requires total internal reflection, hence \(n_{1}\gt n_{2}\) — but only slightly. A fibre is weakly guiding, with a fractional index difference
\(\Delta=\dfrac{n_{1}-n_{2}}{n_{1}}\approx0.002\ \text{to}\ 0.01\)
Taking a typical \(n_{1}=1.48\) and \(n_{2}=1.46\),
\(NA=\sqrt{1.48^{2}-1.46^{2}}=\sqrt{2.1904-2.1316}=\sqrt{0.0588}=0.242\)
— an acceptance half-angle of about 14°.
| Fibre | Typical NA | Acceptance half-angle |
|---|---|---|
| Multimode step index | 0.2 – 0.5 | 12° – 30° |
| Single mode | 0.1 – 0.15 | 6° – 9° |
Why the other options are impossible. NA = 1 would mean an acceptance angle of 90° — light entering from any direction whatever — which would require \(n_{1}^{2}-n_{2}^{2}=1\), an index contrast no glass fibre has. NA > 1 is mathematically impossible for a sine. NA = 0 would mean no light accepted at all, which is the case only when core and cladding indices are equal, so there is no guidance.
What NA controls in practice. A larger NA collects more light from an LED and tolerates looser alignment, so coupling efficiency improves — but it also admits rays over a wider range of angles, and those rays travel different path lengths, producing intermodal dispersion that limits bandwidth. Single-mode fibre takes the opposite choice deliberately: a small core and a small NA, so only one path exists, at the cost of demanding a laser source and precise splicing.
Note what NA does not depend on : only the two refractive indices, never the core diameter. A fatter core gathers more light because of its area, but its acceptance angle is unchanged.
Hence, the numerical aperture of an optical fibre is < 1.
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?
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.
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In linearly polarized modes traversing in the optical fibers the LP01 is exactly equal to :
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:
