Snell's Law Calculator

Snell's Law Explained

Snell's law describes how light bends when it crosses the boundary between two materials with different refractive indices.

$$n_1 \sin\theta_1 = n_2 \sin\theta_2$$

The normal is the line perpendicular to the boundary between the two media. When light moves into a denser medium (n₂ > n₁), it bends toward the normal; moving into a less dense medium, it bends away from the normal.

Worked Example: Light Entering Water

Using the calculator's defaults — light traveling from air ($n_1 = 1.0$) into water ($n_2 = 1.33$) at a 30° incident angle — Snell's law gives $\sin\theta_2 = \frac{1.0 \times \sin(30°)}{1.33} \approx 0.376$, so $\theta_2 \approx 22.1°$. The ray bends toward the normal, exactly as expected when entering a denser medium — this is the same effect that makes a straw in a glass of water look bent at the surface.

Total Internal Reflection and the Critical Angle

Going the other way — from a denser medium into a less dense one — light bends away from the normal, and beyond a certain incident angle it can't refract out at all. That threshold is the critical angle:

$$\theta_c = \arcsin\left(\frac{n_2}{n_1}\right)$$

Past the critical angle, all the light reflects back into the denser medium instead of crossing the boundary — this is total internal reflection, the principle that keeps light trapped inside a fiber optic cable as it travels.

Refractive Index of More Materials

The calculator's own dropdowns cover the most common media, but here are more reference values (measured at the sodium D line, 589 nm, the standard wavelength optical references use) for materials you may run into:

Material	Refractive Index (n)
Ethanol	1.36
Quartz	1.46
Fused Silica	1.458
Crown Glass	1.52
Human Eye — Cornea	1.376
Human Eye — Lens	1.406
Table Salt (NaCl)	1.544
Amber	1.55
Emerald	1.58
Flint Glass	1.62
Ruby	1.76
Zircon	1.92
Cubic Zirconia	2.16
Moissanite	2.65
Silicon (infrared)	3.48

Values are typical room-temperature figures drawn from standard optical reference sources — the CRC Handbook of Chemistry and Physics and refractiveindex.info, a freely accessible, citation-backed refractive index database maintained by Dr. Mikhail Polyanskiy and widely used in the optics research community. Real samples vary somewhat with purity, temperature, and the exact wavelength measured.

A Brief History of Snell's Law

Willebrord Snellius derived the law bearing his name around 1621, though historical evidence suggests the 10th-century scholar Ibn Sahl had already worked out an equivalent relationship centuries earlier, and René Descartes published his own derivation in 1637 (which is why some countries call it Descartes' law instead). The law was placed on firmer theoretical footing later, once the wave nature of light and its varying speed in different media were properly understood.

Common Snell's Law Mistakes

Measuring the angle from the boundary surface instead of the normal is the single most common error — Snell's law always uses the angle from the perpendicular, not from the surface itself. Forgetting to check for total internal reflection before computing $\theta_2$ is another frequent mistake; if $n_1 > n_2$ and the incident angle exceeds the critical angle, there simply is no valid refraction angle, since $\sin\theta_2$ would need to exceed 1. Mixing up which medium is "1" and which is "2" is a third common slip, since swapping them changes whether the light should bend toward or away from the normal.

Optics Terms You Should Know

Refractive Index (n) — a measure of how much a material slows light down relative to a vacuum.

Normal — the imaginary line perpendicular to a boundary surface, used as the reference for measuring angles.

Critical Angle — the incident angle beyond which total internal reflection occurs, only defined when going from a denser to a less dense medium.

Total Internal Reflection — complete reflection of light at a boundary, with no light transmitted into the second medium.

Refractive index values given here are typical for visible light; actual values vary slightly with wavelength (an effect called dispersion) and temperature.