Refraction

When a wave passes from one medium into another, it usually changes speed. If it strikes the boundary at an angle, this change in speed causes the wave to change direction — a phenomenon known as refraction. Refraction is responsible for a host of familiar effects, from the apparent bending of a straw in a glass of water to the focusing of light in a microscope and the twinkling of stars through the restless air above our heads.

This lesson develops the quantitative physics of refraction at A-Level: the refractive index, Snell's law, and the geometry of refraction at a boundary between two transparent media.

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What Refraction Is and What It Is Not

Refraction is the change in direction of a wave as it passes from one medium to another, caused by a change in its speed. Note carefully what refraction is not:

• It is not reflection (that is the bouncing back of a wave at a boundary).
• It is not diffraction (that is the bending of a wave around an obstacle or through an aperture — Lesson 10).
• It does not change the wave's frequency — only its speed and wavelength change.

The frequency is set by the source and does not change across a boundary (otherwise energy would not be conserved in a steady-state wave pattern). Since v = fλ and f is constant, a fall in speed must produce a proportional fall in wavelength.

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Refractive Index

The refractive index n of a material is defined as the ratio of the speed of light in vacuum (c) to the speed of light in the material (v):

n = c / v

• c = 3.00 × 10⁸ m s⁻¹, the speed of light in vacuum.
• v = speed of light in the material (m s⁻¹).

Because v ≤ c in any physical medium, n ≥ 1 always.

Medium	Refractive index (for visible yellow light)
Vacuum	1.000 (exactly)
Air (at 20 °C, 1 atm)	1.0003 (usually taken as 1.00)
Water	1.33
Ethanol	1.36
Glass (crown)	1.52
Perspex	1.49
Diamond	2.42

A larger refractive index means light travels more slowly in the medium. Diamond's high refractive index (2.42) is why it sparkles so brightly — light is slowed dramatically and refracted strongly.

Exam Tip: For air, the refractive index is so close to 1 that OCR questions treat air as equivalent to vacuum unless explicitly stated otherwise. "Light passes from air into glass" means n₁ = 1.00, n₂ = 1.52.

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Snell's Law

When a wave passes from a medium of refractive index n₁ into a medium of refractive index n₂, with angles measured from the normal to the boundary (not from the boundary itself), the angles of incidence (θ₁) and refraction (θ₂) are related by Snell's law:

n₁ sin θ₁ = n₂ sin θ₂

This is the fundamental equation of refraction.

flowchart TB
    subgraph Above["Medium 1: n_1 smaller"]
        I[Incident ray at angle theta_1]
        N1[Normal line]
    end
    subgraph Below["Medium 2: n_2 larger"]
        R[Refracted ray at angle theta_2]
        N2[Normal continues]
    end
    I --> B[Boundary surface]
    B --> R
    I -. angle theta_1 .- N1
    R -. angle theta_2 .- N2
    Note[theta_2 is smaller than theta_1: ray bends towards normal]

Direction of Bending

• When light passes from a less dense medium (smaller n) into a more dense medium (larger n), it slows down and bends towards the normal. θ₂ < θ₁.
• When light passes from a more dense medium into a less dense medium, it speeds up and bends away from the normal. θ₂ > θ₁.

Exam Tip: To remember the direction: slow media (high n) bend rays towards the normal. A convenient mnemonic: "into slower, towards normal".

The Normal

The normal is the imaginary line perpendicular to the boundary at the point where the wave meets it. Angles of incidence, reflection and refraction are always measured between the ray and the normal, never between the ray and the boundary. OCR will take marks off for angles measured from the surface.

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Deriving Snell's Law from Wave Speeds

Snell's law can be written in a more physical form. The refractive index ratio equals the speed ratio:

n₁ sin θ₁ = n₂ sin θ₂

Substituting n₁ = c/v₁ and n₂ = c/v₂, the c's cancel:

sin θ₁ / sin θ₂ = v₁ / v₂

In words: the ratio of the sines of the angles equals the ratio of the speeds. This reveals the physical cause of refraction — the wave slows down in the denser medium, and the wavefronts "bunch up" against the boundary, tilting the direction of propagation.

Since f is constant and v = fλ:

λ₁ / λ₂ = v₁ / v₂ = sin θ₁ / sin θ₂

The wavelength therefore also shrinks in the slower medium in the same proportion as the speed.

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Worked Example 1 — Light into Glass