Light Refraction
Light refraction is the bending of a light ray as it passes from one transparent medium into another of different optical density, caused by a change in the wave's speed. The greater the difference in refractive indices between the two media, the more the ray bends toward or away from the normal. Refraction is responsible for phenomena such as the apparent bending of a straw in water, the formation of rainbows, and the focusing action of lenses.
Key Formula
n1 * sin(θ1) = n2 * sin(θ2)
LaTeX: n_1 \sin\theta_1 = n_2 \sin\theta_2
| Symbol | Meaning | Unit |
|---|---|---|
| n₁ | Refractive index of medium 1 | dimensionless |
| θ₁ | Angle of incidence (from normal) | degrees or radians |
| n₂ | Refractive index of medium 2 | dimensionless |
| θ₂ | Angle of refraction (from normal) | degrees or radians |
Worked Example
Problem
A light ray travels in air (n = 1.00) and strikes a glass surface (n = 1.50) at an angle of incidence of 30°. What is the angle of refraction inside the glass?
Solution
Step 1: Write Snell's Law: n₁ sin θ₁ = n₂ sin θ₂ Step 2: Substitute values: 1.00 × sin 30° = 1.50 × sin θ₂ Step 3: sin 30° = 0.500, so 1.00 × 0.500 = 1.50 × sin θ₂ Step 4: sin θ₂ = 0.500 / 1.50 = 0.3333 Step 5: θ₂ = arcsin(0.3333) ≈ 19.47°
Answer
Angle of refraction ≈ 19.5° (ray bends toward the normal upon entering denser glass)
Refractive Indices of Common Materials (for visible light)
| Material | Refractive Index (n) | Speed of Light (m/s) | Example Use |
|---|---|---|---|
| Vacuum | 1.000 | 3.00 × 10⁸ | Space baseline |
| Air | 1.003 | 2.99 × 10⁸ | Atmosphere |
| Water | 1.333 | 2.25 × 10⁸ | Aquariums, pools |
| Crown Glass | 1.520 | 1.97 × 10⁸ | Eyeglass lenses |
| Diamond | 2.417 | 1.24 × 10⁸ | Jewellery sparkle |
Interactive Tools
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Related Terms
Snell's Law
Snell's Law (also called the law of refraction) states that the product of the refractive index and the sine of the angle of incidence is constant across the interface between two media: n₁ sin θ₁ = n₂ sin θ₂. It quantitatively describes how a light ray changes direction when it transitions between media of different optical densities. Snell's Law is the cornerstone of lens design, fibre optic engineering, and the correction of refractive vision errors.
Total Internal Reflection
Total Internal Reflection (TIR) occurs when a light ray travelling through a denser medium strikes the boundary with a less dense medium at an angle greater than the critical angle, causing the ray to be completely reflected back into the denser medium rather than refracted out. The critical angle θ_c is defined as sin θ_c = n₂/n₁, where n₁ > n₂. TIR is the operating principle behind optical fibres, diamonds' brilliance, and binocular prisms.
Lens (Optics)
In optics, a lens is a transmissive optical element, typically made of glass or transparent plastic, that refracts light to converge or diverge rays, thereby forming images. Lenses work by exploiting the refraction of light at curved surfaces, and their shape (convex or concave) determines whether rays are brought together (converging) or spread apart (diverging). Lenses are fundamental components of eyeglasses, cameras, microscopes, telescopes, and the human eye itself.
From Latin "refringere" meaning "to break up" or "to break again" (re- = again, frangere = to break). The word entered English in the 17th century. Willebrord Snellius (1580–1626) discovered the quantitative law, and René Descartes published it in 1637.