Describe the use of optical fibres, particularly in telecommunications

3.2.2 Refraction of Light – Use of Optical Fibres in Telecommunications

1. Key Definitions

• Normal: an imaginary line perpendicular to the surface at the point of incidence.
• Angle of incidence \( \theta_i \): the angle between the incident ray and the normal.
• Angle of refraction \( \theta_r \): the angle between the refracted ray and the normal.
• Refractive index \( n \): the ratio of the speed of light in vacuum (\(c\)) to its speed in a material (\(v\)):

  \[

  n=\frac{c}{v}

  \]

  Typical values: \(n{\text{glass}}\approx1.5\), \(n{\text{air}}=1.00\).

2. Snell’s Law

When a ray passes from medium 1 (index \(n1\)) to medium 2 (index \(n2\)), the angles are related by

\[

n1\sin\thetai = n2\sin\thetar

\]

This law predicts how the ray bends at the interface and is the basis for all later calculations.

3. Critical Angle and Total Internal Reflection (TIR)

• If light travels from a higher‑index medium (\(n1\)) to a lower‑index medium (\(n2\)), the refracted ray bends away from the normal.
• When the incident angle exceeds a certain value, the refracted ray disappears and the light is reflected back into the first medium – this is total internal reflection.

Critical‑angle formula (derived from Snell’s law with \(\theta_r=90^{\circ}\)):

\[

\thetac = \sin^{-1}\!\left(\frac{n2}{n_1}\right)

\]

Example (glass core / glass cladding):

\[

n{\text{core}} = 1.48,\qquad n{\text{clad}} = 1.46

\]

\[

\theta_c = \sin^{-1}\!\left(\frac{1.46}{1.48}\right)=\sin^{-1}(0.9865)\approx 80^{\circ}

\]

Any ray that meets the core–cladding interface at an angle \(>80^{\circ}\) (measured from the normal) is totally internally reflected.

4. Numerical Aperture (NA) and Acceptance Angle

The numerical aperture quantifies the range of external angles that will be captured by the fibre:

\[

\text{NA}= \sqrt{n{\text{core}}^{2}-n{\text{clad}}^{2}}

\]

For light entering from air (\(n{\text{air}}=1\)), the maximum acceptance angle \(\theta{\max}\) is

\[

\theta{\max}= \sin^{-1}\!\left(\frac{\text{NA}}{n{\text{air}}}\right)

\]

Example using the indices above:

\[

\text{NA}= \sqrt{1.48^{2}-1.46^{2}}=\sqrt{0.0588}\approx0.24

\]

\[

\theta_{\max}= \sin^{-1}(0.24)\approx 14^{\circ}

\]

Only light that enters the fibre within ±14° of the fibre axis will be guided.

5. Why Light Is Guided in an Optical Fibre

• The core has a higher refractive index than the cladding, so rays that satisfy the acceptance‑angle condition undergo repeated TIR at the core–cladding interface.
• Each internal reflection keeps the ray confined to the core, allowing it to travel long distances with very little loss (attenuation).

6. Structure of an Optical Fibre

• Core – central glass (or plastic) cylinder, \(n_{\text{core}}\approx1.48\), diameter 8–62.5 µm depending on type.
• Cladding – outer layer of slightly lower index, \(n_{\text{clad}}\approx1.46\), provides the TIR condition.
• Jacket – protective polymer coating that shields the fibre from mechanical damage and moisture.

7. Types of Optical Fibre

8. Link to Thin‑Lens Concepts (3.2.3)

• A converging lens can focus light from a source onto the fibre end‑face, ensuring that the entering rays satisfy the acceptance‑angle condition.
• Using the lens formula \(\displaystyle \frac{1}{f}= \frac{1}{u}+\frac{1}{v}\), the teacher can show how to choose the object distance \(u\) so that the image distance \(v\) coincides with the fibre tip.
• This demonstrates the practical relevance of focal length, image formation, and ray diagrams – a direct bridge to the thin‑lens part of the syllabus.

9. Role of Optical Fibres in Telecommunications

• Signal carrier: pulses of light generated by lasers (long‑haul) or LEDs (short‑haul).
• Attenuation: modern single‑mode fibres lose ≈ 0.2 dB km⁻¹ at 1550 nm, allowing signals to travel hundreds of kilometres without repeaters.
• Bandwidth: extremely high – a single fibre can carry terabits per second using wavelength‑division multiplexing (WDM).
• Immunity to EMI: light is not affected by electromagnetic fields, making fibres ideal for noisy environments.
• Weight & size: typical outer diameter ≈ 125 µm; far lighter and thinner than copper cables.

10. Comparison with Copper Cables

11. Classroom Demonstration – Total Internal Reflection (AO3)

Apparatus: laser pointer, rectangular water tank (or clear acrylic block), protractor, white paper.

1. Fill the tank with water (\(n_{\text{water}}\approx1.33\)).
2. Shine the laser at the water–air interface and measure the angle of incidence \(\theta\) from the normal.
3. Increase \(\theta\) until the beam no longer emerges into the air but is reflected back into the water – this is the critical angle.
4. Record the angle and compare with the calculated value

   \(\thetac=\sin^{-1}(n{\text{air}}/n_{\text{water}})\approx48^{\circ}\).

5. Discuss how the same principle operates in a glass‑core optical fibre, where the higher indices give a larger critical angle and thus a wider acceptance cone.

Learning outcomes: measuring angles, applying Snell’s law, understanding TIR, and linking the physics to real‑world fibre optics.

12. Key Points to Remember (Revision Checklist)

• Refractive index: \(n=c/v\).
• Snell’s law: \(n1\sin\thetai=n2\sin\thetar\).
• Critical angle: \(\thetac=\sin^{-1}(n2/n1)\); TIR occurs for \(\thetai>\theta_c\).
• Numerical aperture: \(\text{NA}= \sqrt{n{\text{core}}^{2}-n{\text{clad}}^{2}}\); acceptance angle \(\theta_{\max}= \sin^{-1}(\text{NA})\).
• Light is guided because the core‑cladding pair satisfies \(n{\text{core}}>n{\text{clad}}\) and the incident rays meet the acceptance‑angle condition.
• Single‑mode fibres → long distance, high capacity; Multi‑mode fibres → short distance, cheaper.
• Advantages over copper: very low attenuation, huge bandwidth, immunity to EMI, light weight, small size.
• Thin‑lens optics are used to couple light efficiently into the fibre end‑face.
• Practical skills: calculating \(\thetac\) and \(\theta{\max}\), measuring acceptance angles, performing a TIR demonstration.