---
title: "OFC vs cable and radio; NA"
subject: "Propagation and Antenna"
chapter: 6
key: "semester_6/propagation_and_antenna:ofc-vs-cable-radio-na"
source: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/ofc-vs-cable-radio-na
site: BCT Engineering
---

# OFC vs cable and radio; NA

Propagation and Antenna · Chapter 6: Optical Fibres

- Asked in: 2073 Bhadra, 4+4 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/propagation_and_antenna/ofc-vs-cable-radio-na
- Whole chapter: https://www.bctengineer.com/md/semester_6/propagation_and_antenna/chapter-6

## Question

Compare optical fiber communication with cable and radio communication systems. Describe numerical aperture (NA) in optical communication system.

## 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.

## Answer

#### 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.

```text
            \  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:

```text
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°.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which system supports mobile users?
   A. Optical fibre
   B. Coaxial cable
   C. Twisted pair
   D. Radio
   Answer: D. Fibre and cables are fixed. (Key point: Mobility)

2. How does security compare?
   A. Fibre is very high; radio is easy to intercept
   B. Radio is the most secure
   C. All are equal
   D. Coaxial is the most secure
   Answer: A. Fibre does not radiate. (Key point: Security)

3. Which relation gives NA?
   A. n0 sin(theta_a) = n1 sin(phi_c)
   B. n0 sin(theta_a) = n1 cos(phi_c), with sin(phi_c) = n2/n1
   C. n0 sin(theta_a) = n2 cos(phi_c)
   D. n0 cos(theta_a) = n1 cos(phi_c)
   Answer: B. This gives NA = sqrt(n1^2 - n2^2). (Key point: NA derivation)

4. What does the cone of half-angle theta_a represent?
   A. Light inside it leaks
   B. The critical angle
   C. Light inside it is guided
   D. The cladding
   Answer: C. theta_a = sin^-1(NA). (Key point: Acceptance cone)

## Related in Propagation and Antenna

- [OFC block diagram vs cable](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aofc-block-diagram-vs-cable) — Propagation and Antenna, chapter 6
- [Elements of optical communication system](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aoptical-communication-elements) — Propagation and Antenna, chapter 6, asked 3×
- [Numerical aperture and dispersion](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Ana-and-dispersion) — Propagation and Antenna, chapter 6
- [Optical fibre system vs wireless](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aofc-working-vs-wireless) — Propagation and Antenna, chapter 6
- [Multimode vs single mode; NA derivation](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Amultimode-vs-single-na-derivation) — Propagation and Antenna, chapter 6
- [Acceptance angle and NA of step-index fibre](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Aacceptance-angle-na-step-index) — Propagation and Antenna, chapter 6, asked 2×

## Related in other subjects

- [Derive numerical aperture of optical fiber](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Ana-derivation-optical-fiber) — Engineering Physics, chapter 6, asked 4×
- [Optical fiber, NA, single vs multimode](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aoptical-fiber-na-acceptance-mode-comparison) — Engineering Physics, chapter 6
- [Coaxial cable vs optical fiber](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acoax-vs-fiber) — Data Communication, chapter 4
- [Communication system; optical fiber merits](https://www.bctengineer.com/question.md?key=semester_2%2Fbasic_electronics_engineering%3Adefine-comm-optical-merits) — Basic Electronics Engineering, chapter 5