EngineerHub.orgWhat this simulator teaches
Refraction follows one compact rule, but the geometry produces many familiar effects. The same Snell-law relationship explains why rays bend toward or away from the normal, why total internal reflection occurs, why objects under water look shallower, and why a prism separates colors.
snell's lawcritical angletotal internal reflectionfresnel reflectionglass slabapparent depthprism deviationdispersion
Select refraction model6 visual learning modes
Single-interface controls
Single optical interface
Snell's law determines the transmitted angleSingle interface — bending is measured from the normal
The dashed line is the surface normal. Change either refractive index or the incidence angle and watch the transmitted ray rotate according to Snell's law.
n₁ sinθ₁ = n₂ sinθ₂
Incident / transmitted rayReflected / reference raySurface normalGeometry / result marker
Four ideas behind refraction
01 / Snell's lawThe angles are measured from the normal, not from the surface. For two transparent media, n₁sinθ₁ = n₂sinθ₂.
02 / Optical speedThe phase speed in a medium is v = c/n. Frequency stays fixed across a stationary boundary, so wavelength changes in proportion to speed.
03 / Critical angleWhen light travels from higher n to lower n, the refracted angle reaches 90° at θc = asin(n₂/n₁). Above it there is no propagating transmitted ray.
04 / DispersionReal materials have wavelength-dependent refractive index. In normal dispersion, shorter visible wavelengths usually have larger n and therefore bend more strongly in a prism.
Model assumptions & limits
The geometric ray paths assume homogeneous media and flat interfaces except for the prism faces. Refractive indices are treated as real numbers; absorption is not solved.
The single-interface mode reports ideal power reflectance for unpolarized light using the average of the s- and p-polarized Fresnel reflectances. At total internal reflection, the propagating transmitted power is zero in this ideal lossless model.
The familiar d_app ≈ d(n_observer/n_object) expression is the near-normal, paraxial limit. This page also back-projects the selected finite-angle refracted ray: d_app = d tanθ_object / tanθ_observer.
The prism calculation treats a homogeneous prism in a uniform surrounding medium. It applies Snell's law independently at the two faces using signed face-normal angles; a negative second-face angle is valid and means the ray lies on the opposite side of that normal. It reports total internal reflection when no propagating exit ray exists.
Fused silica uses the Malitson room-temperature Sellmeier equation. SCHOTT N-BK7 uses SCHOTT's published Sellmeier dispersion constants. These are educational material models; precision optical design should use the manufacturer's current melt-specific data.
Background & FAQ
If n₂ is greater than n₁, Snell's law requires sinθ₂ to be smaller than sinθ₁. The transmitted angle therefore moves closer to the normal.
No for a stationary boundary. Frequency is continuous across the interface. The phase speed changes to c/n, so wavelength changes instead.
No. Total internal reflection requires propagation from the higher-index side toward a lower-index medium and an incidence angle above the critical angle.
When the material on both sides is the same and the two faces are parallel, the second refraction cancels the first angular change. The outgoing ray is parallel to the incoming ray but laterally displaced.
Rays leaving the denser medium bend away from the normal. Your eye extrapolates those rays backward in straight lines, placing the apparent source closer to the interface.
For normal optical dispersion, refractive index is higher at shorter visible wavelengths. Snell's law therefore produces slightly stronger bending for blue/violet light than for red light.