--- title: "Huygens's principle and the laws of reflection and refraction" description: "Use Huygens's wavelet construction for plane wavefronts at stationary boundaries between uniform isotropic materials. Equal-time geometry gives reflection and Snell's law for a propagating transmitted" canonical: https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w source: https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w.md retrieved: 2026-11-12 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # Huygens's principle and the laws of reflection and refraction Use Huygens's wavelet construction for plane wavefronts at stationary boundaries between uniform isotropic materials. Equal-time geometry gives reflection and Snell's law for a propagating transmitted ray, using the wave speed in each material. Subject: Science · Area: Waves, Light & Sound · Ages 18 to 19 Page: https://lightmysky.com/learn/science/huygenss-principle-and-the-laws-of-reflection-and-refraction-mt_xxdniF2__w ## Ready when they can - Constructs a refracted wavefront from wavelets and derives Snell's law - Relates refractive index to the speed of light in the material - Explains why the frequency is unchanged on crossing a boundary but the wavelength is not ## Lesson: Wavelets that explain mirrors and bending light You have used rays, normals and n = c/v. A wavefront joins points at the same wave phase. In a uniform isotropic material, rays are perpendicular to it. In Huygens's construction, each front point produces a secondary wavelet. After time t, its radius is v*t. The forward tangent envelope of these wavelets gives the next front. For oblique incidence, take a plane front AB approaching a flat, stationary boundary. A reaches it first. After time t, B reaches boundary point C. From A, draw a transmitted wavelet of radius v2*t. Draw its tangent from C, touching at D. DC is the refracted front. BC = v1*t is perpendicular to AB; AD = v2*t is perpendicular to DC. This construction requires a propagating transmitted wave. Let L = AC, the shared boundary segment. Measure ray angles θ1 and θ2 from the normal. Because rays are perpendicular to fronts, these equal the corresponding front-boundary angles. The right triangles give sin(θ1) = BC/L = v1*t/L and sin(θ2) = AD/L = v2*t/L. Here sin(θ) is the opposite side divided by the hypotenuse in a right triangle. *(drawing: The cells show the algebra from the two triangles. They do not draw the wavefronts.)* Both triangles use the same time t and boundary length L. Dividing each sine relation by its own speed gives sin(θ1)/v1 = sin(θ2)/v2 = t/L. Since n1 = c/v1 and n2 = c/v2, multiplying by c gives Snell's law: n1*sin(θ1) = n2*sin(θ2). For reflection, both wave speeds are equal, so the equal-time construction gives equal incidence and reflection angles. The law of reflection uses the local normal: the reflected angle equals the incident angle. Both rays and that normal lie in one plane. On a smooth plane mirror, local normals align, so parallel incoming rays reflect in one direction. Rough reflecting surfaces have varying local normals, so reflected rays leave in different directions. Refractive index is n = c/v, where c is vacuum light speed and v is light's phase speed in the material. Rearrange to v = c/n. For c = 300 million metres per second and n = 1.25, v = 300/1.25 = 240 million metres per second. Use matching speed units in the ratio. For monochromatic light transmitted across a stationary linear boundary, cycles match in time at the boundary, so frequency f stays fixed. From v = f*λ, wavelength λ = v/f. Entering ordinary glass from air lowers speed and wavelength. At normal incidence, direction stays unchanged even though speed and wavelength change. The normal is perpendicular to the boundary. A ray's acute surface angle α and normal angle θ therefore satisfy α + θ = 90 degrees. A surface angle of 20 degrees gives θ = 70 degrees. Use the normal angle in Snell's law. The two readings coincide at 45 degrees, but their reference lines still differ. **Recap.** Equal-time wavelet geometry gives reflection and Snell's law. Measure angles from the normal. At a stationary linear boundary, frequency stays fixed and wavelength follows speed. *Lesson, questions and flashcards written for this dataset.* ## Practice 8 questions on this page, each with its working shown. ## Needs first - [Superposition and Stationary Waves](https://lightmysky.com/learn/science/superposition-and-stationary-waves-mt_AIxA2TYGJN) - [Refraction and lenses](https://lightmysky.com/learn/science/refraction-and-lenses-mt_u8GKuBMmzC) ## Optional connections - [The Doppler Effect and Shock Waves](https://lightmysky.com/learn/science/the-doppler-effect-and-shock-waves-mt_UVfD_coqh6) ## Opens up - [Curved Mirrors, the Mirror Equation and Real Images](https://lightmysky.com/learn/science/curved-mirrors-the-mirror-equation-and-real-images-mt_7XqB2umthJ) - [Thin lenses and the lens maker's equation](https://lightmysky.com/learn/science/thin-lenses-and-the-lens-makers-equation-mt_FXOcC5mpIM) - [Total Internal Reflection, Optical Fibres and Dispersion](https://lightmysky.com/learn/science/total-internal-reflection-optical-fibres-and-dispersion-mt_ZNSZMLkOD_)