---
title: "Optical fiber, NA, single vs multimode"
subject: "Engineering Physics"
chapter: 6
key: "semester_1/engineering_physics:optical-fiber-na-acceptance-mode-comparison"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/optical-fiber-na-acceptance-mode-comparison
site: BCT Engineering
---

# Optical fiber, NA, single vs multimode

Engineering Physics · Chapter 6: Laser and Fiber Optics

- Asked in: 2074 Chaitra, 5 marks
- Video: [Single-mode Optical fiber and Multi-mode Optical Fiber in Optical Fiber Communication](https://www.youtube.com/watch?v=KW3HSJthFws) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/optical-fiber-na-acceptance-mode-comparison
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-6

## Question

What is optical fiber? Explain numerical aperture and acceptance angle. Also compare the attenuation property, efficiency and cost of single mode and multimode optical fibers.

## Short answer

An optical fiber is a glass/plastic strand guiding light by total internal reflection. Numerical aperture NA = n₀ sinθ₀ = √(n₁²−n₂²) measures light-gathering ability; acceptance angle θ₀ is the maximum entrance angle for guided rays. Single-mode fiber has lower attenuation (0.2–0.5 dB/km), higher long-haul efficiency, but higher connector costs; multimode has higher attenuation (1–3 dB/km), lower bandwidth, cheaper system for short links.

## Answer

#### Optical fiber
An optical fiber is a thin strand of glass or plastic that carries light signals by total internal reflection. It has a core (index n₁) surrounded by a cladding (index n₂ < n₁).

#### Acceptance angle and numerical aperture
- **Acceptance angle θ₀:** the largest angle to the fiber axis at which a ray from air can enter the core and be guided. The cone of half-angle θ₀ is the acceptance cone.
- **Numerical aperture:** NA = n₀ sin θ₀ = √(n₁² − n₂²) = n₁ √(2Δ), with Δ = (n₁ − n₂)/n₁. It measures the light-collecting ability of the fiber.

```text
   rays outside cone are lost
      \   |  /  
       \ θ0 /      ---------- cladding n2
 air    \|/  -------core n1--------> guided
 n0=1   /|\  ---------------------
       / | \
```
**Derivation in brief:** a ray with θ₁ inside the core hits the cladding boundary at 90° − θ₁. At the critical angle sin φ_c = n₂/n₁, and Snell's law at the entrance gives sin θ₀ = √(n₁² − n₂²).

#### Single-mode and multimode fibers
| Property | Single mode | Multimode |
|---|---|---|
| Core diameter | 8 to 10 µm | 50 to 62.5 µm |
| Modes | One | Hundreds |
| Attenuation | Low, about 0.2 to 0.5 dB/km at 1310/1550 nm | Higher, about 1 to 3 dB/km at 850 nm |
| Dispersion | Very low, high bandwidth | Intermodal dispersion limits bandwidth |
| Efficiency | Best for long distance; coupling into the small core needs a laser and precise alignment | Easy coupling, efficient with an LED over short distance |
| Cost | Cable is cheap per metre, but lasers and connectors are costly | Cable somewhat dearer per metre; LEDs and connectors cheap, so the system is cheaper for short links |
| Use | Long-haul telecom, undersea cables | LAN, buildings, short links |

## Check yourself

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

1. The acceptance angle is:
   A. Cladding angle
   B. Angle of the cone's full width
   C. Maximum angle to the axis for guided entry
   D. Critical angle
   Answer: C. Rays within it are guided. (Key point: Acceptance angle)

2. Which has lower attenuation?
   A. Equal
   B. Neither
   C. Multimode
   D. Single mode
   Answer: D. Single-mode: 0.2 to 0.5 dB/km. (Key point: Attenuation)

3. For short links, which system is cheaper?
   A. Neither
   B. Equal
   C. Multimode, due to LEDs and connectors
   D. Single mode
   Answer: C. Multimode couples easily with an LED. (Key point: Cost)

## Related in Engineering Physics

- [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×
- [Acceptance angle of fiber in a liquid](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Afiber-acceptance-angle-liquid-index-change) — Engineering Physics, chapter 6
- [Glass-clad fiber numerical aperture](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Afiber-na-glass-clad-numerical) — Engineering Physics, chapter 6
- [Acceptance angle of fiber in water](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Afiber-acceptance-angle-water) — Engineering Physics, chapter 6
- [Physical significance of numerical aperture](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anumerical-aperture-significance-dependence) — Engineering Physics, chapter 6

## Related in other subjects

- [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×
- [Fibre losses; multimode vs single mode](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Afiber-losses-multimode-vs-single) — Propagation and Antenna, chapter 6
- [Light propagation; define NA and acceptance angle](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alight-propagation-define-na-acceptance) — Propagation and Antenna, chapter 6