Laws of Refraction
Simple Explanation
The laws of refraction precisely describe how light bends at a boundary: (1) the incident ray, refracted ray, and normal all lie in the same plane, and (2) Snell's law relates the angles of incidence and refraction to the refractive indices of the two media.
Why Do We Need It?
Snell's law is the quantitative tool that lets you actually calculate refraction angles, rather than just qualitatively describing that light bends.
Formula
Snell's Law (Law of Refraction)
n₁ sinθ₁ = n₂ sinθ₂
When light crosses the boundary between two media, the product of each medium's refractive index and the sine of the angle (measured from the normal) is the same on both sides.
- n₁, n₂
- — Refractive indices of the first and second media
- θ₁
- — Angle of incidence, measured from the normal, in the first medium
- θ₂
- — Angle of refraction, measured from the normal, in the second medium
When to use it: Use to find an unknown angle of incidence or refraction, or an unknown refractive index, when light crosses a boundary between two media.
Worked Example
Finding the angle of refraction
Light travels from air (n₁ = 1.00) into glass (n₂ = 1.50) at an angle of incidence of 40° (sin40° ≈ 0.643). Find the angle of refraction.
Why Does This Work?
Snell's law follows directly from the wave nature of light: as a wavefront crosses the boundary, its frequency stays constant, but its speed (and therefore wavelength) changes in the new medium — working through the geometry of this speed change produces the sine relationship exactly.
Real-Life Example
Designing camera lenses
Camera lens designers use precise calculations to control exactly how light bends through each lens element.
Snell's law lets engineers precisely predict and control how light refracts through each lens surface, which is essential for designing lenses that focus light accurately and minimise distortion.
Practice
Light travels from air (n₁ = 1.00) into water (n₂ = 1.33) at an angle of incidence of 50° (sin50° ≈ 0.766). Find sinθ₂.
MediumCommon mistake
Mixing up which medium's refractive index and angle go where in the formula — always match n₁ with θ₁ (the medium and angle the light is COMING FROM) and n₂ with θ₂ (the medium and angle the light is ENTERING).
Quick Review
- Snell's law: n₁ sinθ₁ = n₂ sinθ₂.
- The incident ray, refracted ray, and normal all lie in the same plane.
- Snell's law lets you calculate unknown angles or refractive indices precisely.