Refraction

Refraction

The change in direction of a wave when it passes through a boundary between mediums of different density, caused by a change in the speed of the wavefront

Why does refraction occur?

One side of the wavefront hits the boundary and changes speed before the other side, causing the wave to change direction

Angle of incidence

The angle between the approaching incident ray and the normal (drawn at 90° to the boundary)

Angle of refraction

The angle between the refracted ray leaving the boundary and the normal

Light entering a more optically dense medium (e.g. air → glass)

Speed decreases; wavelength decreases; ray bends towards the normal; angle of refraction < angle of incidence

Light entering a less optically dense medium (e.g. glass → air)

Speed increases; wavelength increases; ray bends away from the normal; angle of refraction > angle of incidence

What happens to frequency during refraction?

Frequency does not change — only speed and wavelength change; the colour of the wave stays the same

What happens when a light ray hits a boundary at exactly 90°?

The whole wavefront enters the boundary at the same time so the ray passes straight through without changing direction

Refractive index (n)

A dimensionless property of a material measuring how much light slows down when passing through it; n = c/cₛ, where c = speed of light in a vacuum and cₛ = speed of light in the substance

Refractive index equation

n = c / cₛ, where c = 3.00 × 10⁸ m s⁻¹ (speed of light in vacuum) and cₛ = speed of light in the substance (m s⁻¹)

Why is the refractive index always greater than 1?

Because light in a substance always travels slower than in a vacuum, so c/cₛ is always greater than 1

Refractive index of air

Approximately 1 (light does not slow down significantly in air compared to a vacuum); n_air = 1 in calculations

Optically dense material

A material with a high refractive index — it causes light to travel more slowly through it

Snell's Law

n₁ sin θ₁ = n₂ sin θ₂, where n₁ and n₂ are the refractive indices of the two materials, and θ₁ and θ₂ are the angles of incidence and refraction measured from the normal

How to measure angles in Snell's Law

Always measure θ₁ and θ₂ from the normal to the boundary; if given the angle from the boundary, subtract from 90° to get the correct angle

Critical angle (θ_c)

The angle of incidence (in the denser medium) at which the angle of refraction = 90°, so the refracted ray travels along the boundary

Critical angle equation

sin θ_c = n₂/n₁, where n₁ is the refractive index of the denser medium and n₂ is the refractive index of the less dense medium

Effect of refractive index on critical angle

A larger refractive index gives a smaller critical angle; a material with higher n is more likely to produce TIR

What happens when angle of incidence < critical angle?

The ray is refracted and exits the material (partial refraction and partial internal reflection)

What happens when angle of incidence = critical angle?

The refracted ray travels along the boundary (angle of refraction = 90°)

What happens when angle of incidence > critical angle?

Total internal reflection occurs — the ray is reflected back into the denser medium, following the law of reflection (angle of incidence = angle of reflection)

Conditions for total internal reflection (TIR)

(1) The angle of incidence must be greater than the critical angle; (2) the incident refractive index n₁ must be greater than n₂ (the ray must be in the denser medium)

Total internal reflection — law of reflection

Angle of incidence = angle of reflection

Optical fibre — how it works

Monochromatic light enters the end, refracts into the core, then undergoes repeated TIR against the core-cladding boundary until it exits the other end; signals travel long distances without loss of information or speed

Optical fibre — three main components

(1) Optically dense core (glass or plastic); (2) lower optically dense cladding surrounding the core; (3) outer protective sheath

Step-index fibre

An optical fibre where the refractive index increases in steps from the outside (cladding) to the centre (core); TIR only occurs when n_cladding < n_core

Role of cladding in an optical fibre

Protects the core from damage; prevents signal degradation by stopping light from escaping the core; keeps signals secure and maintains signal quality; keeps the core separate from other fibres to prevent information crossover

Material dispersion

Occurs when white (non-monochromatic) light is used in a fibre; different wavelengths travel at different speeds in the medium, causing the pulse to broaden; violet light travels slowest and undergoes more reflections

Why does violet light take longer to travel down an optical fibre?

Violet has the shortest wavelength and travels slowest in the medium; its smaller angle of incidence leads to more reflections per unit length, so it takes longer to reach the end

Modal dispersion

Occurs with monochromatic light when different parts of the wavefront hit the boundary at different angles, undergoing TIR a different number of times and arriving at the end at slightly different times; more prominent in wider cores

Pulse broadening

When pulses emerge from the fibre longer than when they entered; caused by both material and modal dispersion; can lead to merging of pulses, distorting information and reducing signal amplitude

Signal absorption in optical fibres

The fibre absorbs some of the signal's energy, reducing its amplitude and potentially causing loss of transmitted information

How to reduce absorption in optical fibres

Use an extremely transparent core; use optical fibre repeaters to regenerate the pulse before significant absorption occurs

How to reduce pulse broadening in optical fibres

Use a very narrow core; use a monochromatic light source; use optical fibre repeaters; use a single-mode fibre (only one wavelength passes through) to reduce multipath modal dispersion

Single-mode fibre

An optical fibre with a very narrow core allowing only a single wavelength of light, reducing multipath modal dispersion and pulse broadening