Refraction and Total Internal Reflection

The refractive index ($n$) of a material describes how much light slows down in that medium:

$\boxed{n = \frac{c}{v}}$

Where:

• $n$ = refractive index (dimensionless)
• $c$ = speed of light in vacuum ($3 \times 10^8$ m/s)
• $v$ = speed of light in the medium

$n \geq 1$ for all materials. Vacuum: $n = 1$. Air: $n \approx 1.00$.

$\boxed{n_1 \sin\theta_1 = n_2 \sin\theta_2}$

Where $\theta_1$ and $\theta_2$ are measured from the normal.

Alternatively: $\frac{\sin\theta_1}{\sin\theta_2} = \frac{n_2}{n_1} = \frac{v_1}{v_2}$

When Light Enters a Denser Medium ($n_2 > n_1$)

• Speed decreases
• Wavelength decreases
• Light bends towards the normal ($\theta_2 < \theta_1$)

When Light Enters a Less Dense Medium ($n_2 < n_1$)

• Speed increases
• Wavelength increases
• Light bends away from the normal ($\theta_2 > \theta_1$)

Frequency never changes during refraction.

Occurs when light travels from a denser to a less dense medium and the angle of incidence exceeds the critical angle.

Critical Angle

$\boxed{\sin\theta_c = \frac{n_2}{n_1}}$

For light going from a medium to air ($n_2 = 1$): $\sin\theta_c = \frac{1}{n}$

Conditions for TIR

1. Light must travel from denser to less dense medium
2. Angle of incidence must be greater than the critical angle

Structure

• Core: High refractive index glass/plastic — light travels here
• Cladding: Lower refractive index — ensures TIR keeps light in the core
• Protective sheath: Physical protection

Why Cladding?

• Prevents light leaking between adjacent fibres (cross-talk)
• Protects the core surface from scratches (which would allow light to escape)
• Provides the interface for TIR

Signal Degradation

Absorption: Some light energy is absorbed by the glass, converting to heat. Reduces signal strength.

Dispersion: Two types:

• Modal dispersion: Different rays take different paths (different angles), arriving at different times → pulse broadening. Reduced by using narrow (single-mode) fibres.
• Material dispersion: Different wavelengths travel at different speeds → pulse broadening. Reduced by using monochromatic light (lasers).

Solution: Use repeaters (regenerate signal) at intervals.

• $n = c/v$; higher $n$ = slower light
• Snell's Law: $n_1\sin\theta_1 = n_2\sin\theta_2$
• Critical angle: $\sin\theta_c = n_2/n_1$
• TIR: light from dense → less dense medium, angle > critical angle
• Optical fibres: core (high $n$) + cladding (low $n$) → TIR
• Signal loss: absorption, modal dispersion, material dispersion