---
title: "Acceptance angle of fiber in water"
subject: "Engineering Physics"
chapter: 6
key: "semester_1/engineering_physics:fiber-acceptance-angle-water"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/fiber-acceptance-angle-water
site: BCT Engineering
---

# Acceptance angle of fiber in water

Engineering Physics · Chapter 6: Laser and Fiber Optics

- Asked in: 2069 Asar, 5 marks
- Video: [Calculate the Numerical aperture and Acceptance angle of optical fibre in water and air](https://www.youtube.com/watch?v=nQRMOiH-MdU) — PHYSICS FREAK
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/fiber-acceptance-angle-water
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-6

## Question

An optical fiber has a NA of 0.2 and a cladding refractive index of 1.59. Determine the acceptance angle for the fiber in water which has a refractive index of 1.33.

## Short answer

Acceptance angle in water: θ₀ = sin⁻¹(NA/n₀) = sin⁻¹(0.2/1.33) ≈ 8.65° (core index n₁ ≈ 1.60).

## Answer

For a medium of index n₀ outside the fiber, the acceptance angle θ₀ satisfies n₀ sin θ₀ = NA, where NA = √(n₁² − n₂²) is the value measured from air.

**Given:** NA = 0.2, n₂ = 1.59, n₀ (water) = 1.33.

**Core index (for reference)**
```text
n₁² = NA² + n₂² = 0.04 + 2.5281 = 2.5681
n₁  = 1.6025
```

**Acceptance angle in water**
```text
sin θ₀ = NA / n₀ = 0.2 / 1.33 = 0.1504
θ₀ = sin⁻¹(0.1504) = 8.65°
```
(In air, θ₀ = sin⁻¹ 0.2 = 11.54°; the cone narrows in water because the refractive-index contrast at the entrance face is smaller.)

**Answer: the acceptance angle in water is about 8.65° (core index ≈ 1.60).**

## Check yourself

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

1. A fiber of NA = 0.2 is placed in water (n0 = 1.33). Which gives the acceptance angle?
   A. sin θ0 = NA x n0 = 0.266, so θ0 ≈ 15.4°
   B. sin θ0 = NA/n0 = 0.1504, so θ0 ≈ 8.65°
   C. sin θ0 = NA = 0.2, so θ0 ≈ 11.5°
   D. sin θ0 = n0/NA
   Answer: B. n0 sin θ0 = NA, so the NA is divided by the outside index. (Key point: Acceptance angle relation)

2. Why is the acceptance cone narrower in water than in air?
   A. The refractive-index contrast at the entrance face is smaller, so light bends less into the core
   B. Water absorbs the light
   C. The NA of the fiber becomes smaller in water
   D. Water changes the cladding index
   Answer: A. The fiber's NA is unchanged, but the smaller step in index at the entrance face reduces how much the rays can bend toward the axis. (Key point: Why the cone narrows)

3. Given NA and the cladding index n2, how is the core index n1 found?
   A. n1 = n2 - NA ≈ 1.39
   B. n1 = n2 + NA ≈ 1.79
   C. n1 = sqrt(n2^2 - NA^2) ≈ 1.58
   D. n1 = sqrt(NA^2 + n2^2) ≈ 1.60
   Answer: D. NA^2 = n1^2 - n2^2, so n1^2 = 0.04 + 2.5281 = 2.5681. (Key point: Core index)

## Related in Engineering Physics

- [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
- [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
- [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×
- [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
- [Newton's rings, refractive index of liquid](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Anewton-rings-liquid-refractive-index) — Engineering Physics, chapter 4, asked 2×
- [Refractive index of liquid film by interference](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Acoherent-sources-film-refractive-index-method) — Engineering Physics, chapter 4

## Related in other subjects

- [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×
- [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
- [Light propagation; NA and acceptance angle](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Alight-propagation-na-acceptance-relation) — Propagation and Antenna, chapter 6
- [Refractive index, critical frequency and MUF](https://www.bctengineer.com/question.md?key=semester_6%2Fpropagation_and_antenna%3Arefractive-index-fc-muf) — Propagation and Antenna, chapter 4