- 2073 Bhadra · 4+4 marks
OFC vs cable and radio; NA
Short answer
Optical fibre gives far higher bandwidth, lower attenuation (~0.2 dB/km), EMI immunity and security than cable or radio, but radio offers mobility and cable is cheaper for short links. NA = n0 sin θa = sqrt(n1²−n2²) ≈ n1√(2Δ) measures light acceptance; typical multimode NA 0.2–0.3, single mode 0.1–0.15.
Compare optical fiber communication with cable and radio communication systems. Describe numerical aperture (NA) in optical communication system.
Comparison of optical fibre with cable and radio communication
| Point | Optical fibre | Coaxial / twisted-pair cable | Radio (wireless) |
|---|---|---|---|
| Carrier | Light, ~200 THz | Electrical current | EM waves, kHz–GHz |
| Bandwidth | Very high (Tb/s) | Moderate (MHz–GHz) | Limited by spectrum allotted |
| Attenuation | ~0.2 dB/km | High, rises with frequency | Free space loss, rain, fading |
| Repeater spacing | 80–100 km | 1–5 km | 40–60 km (microwave LOS) |
| EMI / crosstalk | Immune | Affected | Interference, noise |
| Security | Very high | Can be tapped | Easy to intercept |
| Weight / size | Light, thin | Heavy, bulky | No cable |
| Mobility | None | None | Supports mobile users |
| Installation | Costly, needs splicing | Easy | Quick, towers only |
| Licence | Not needed | Not needed | Spectrum licence needed |
In short, fibre is best for high-capacity fixed links, copper cable for short and low-cost connections and power feeding, and radio for mobility, broadcasting and hard-to-reach areas.
Numerical aperture (NA)
Numerical aperture is the light-gathering ability of a fibre, defined as NA = n0 sin θa, where θa is the acceptance angle.
\ θa
n0 \ core n1
-----------*=========================
/ cladding n2 (n2 < n1)
Using Snell's law at the input face and the critical angle at the core–cladding boundary:
n0 sin θa = n1 sin θ1 = n1 cos φc
sin φc = n2/n1
NA = n1 √(1 − n2²/n1²) = √(n1² − n2²) ≈ n1 √(2Δ)
- Only light inside the cone of half-angle θa = sin⁻¹(NA) is guided.
- Larger NA: easier coupling but more modal dispersion.
- Typical NA: 0.1–0.15 for single-mode and 0.2–0.3 for multimode fibre.
- Example: n1 = 1.48, n2 = 1.46 gives NA = 0.2425 and θa = 14°.
✓ Answer checked by Claude Opus 5.5 (high effort)
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