Snell's Law Calculator

Calculate the refraction angle using Snell's law for any two optical media.

Air/vacuum=1.0, Water=1.33, Glass=1.5
Glass=1.5, Diamond=2.42
Please check your inputs and try again.

How Refraction Changes a Light Ray's Direction

Snell's law connects the direction of a ray on the two sides of a boundary between transparent media. The refractive index n=c/v describes how slowly light propagates in a medium relative to vacuum. At a boundary, the wave frequency remains the same while speed and wavelength change, and the ray direction adjusts so that n1sinθ1=n2sinθ2. Both angles are measured from the normal, not from the surface.

If light enters a medium with a larger refractive index, the refracted angle becomes smaller and the ray bends toward the normal. If it enters a lower-index medium, it bends away. The phrase "optically denser" refers to refractive index, not necessarily mass density. A physically denser material does not automatically have the larger optical index.

n1sinθ1 = n2sinθ2
SymbolMeaningWhy it appears / units
n1, n2Refractive indicesDimensionless; depend on medium and wavelength.
θ1Incidence angleMeasured from the normal in medium 1.
θ2Refraction angleMeasured from the normal in medium 2.
θcCritical angleExists only when light travels from higher n to lower n.

When n1>n2, increasing θ1 eventually makes the required sinθ2 exceed 1. That cannot correspond to a transmitted ray, so total internal reflection occurs. The boundary case is θc=sin−1(n2/n1), where the refracted ray would travel along the interface at 90°.

Worked Examples

Example 1: Air to glass: θ₁=45°, n₁=1.0, n₂=1.5
1.0×sin45° = 1.5×sinθ₂
Result: θ₂ = 28.1°
Light bends toward normal entering glass
Example 2: Glass to air: θ₁=45°, n₁=1.5, n₂=1.0
1.5×sin45° = 1.0×sinθ₂
Result: Total Internal Reflection!
Critical angle for glass-air = 41.8°
Example 3: Water to air below the critical angle
n1=1.33, n2=1.00, θ1=30° → sinθ2=1.33sin30°
Result: θ2≈41.7°
The ray bends away from the normal because it is moving from the higher-index medium into the lower-index medium.
Example 4: Glass to water critical angle
n1=1.50, n2=1.33 → θc=sin−1(1.33/1.50)
Result: θc≈62.5°
Incidence angles larger than this value produce total internal reflection for the ideal boundary.

Common Mistakes

⚠️
Measuring angles from the surface

Snell's-law angles are measured from the normal. An angle of 20° from the surface is 70° from the normal.

⚠️
Using the critical-angle formula when n1<n2

Total internal reflection requires travel from a higher refractive index to a lower one. Otherwise n2/n1 exceeds 1 and no critical angle exists.

⚠️
Assuming refractive index is independent of wavelength

Real materials are dispersive. Their refractive index changes with wavelength, which is why a prism can separate colors.

Frequently Asked Questions

What is the critical angle?
The angle of incidence above which total internal reflection occurs: θc = arcsin(n₂/n₁). Light cannot escape into the less-dense medium above this angle.
What is total internal reflection?
When light hits a boundary from a denser medium at angle > critical angle, all light reflects back. This is the principle behind optical fiber cables.
Does light frequency change when it enters another medium?
The frequency stays the same across a stationary boundary because it is fixed by the source and the phase must match at the interface. The wave speed changes with refractive index, so the wavelength changes according to v=fλ. Refraction follows from that change in propagation speed.
Why does light bend toward the normal in higher-index material?
For the same incident angle, Snell's law requires sinθ2=(n1/n2)sinθ1. When n2>n1, that ratio is less than one, so the refracted angle is smaller and therefore closer to the normal.
What happens exactly at the critical angle?
In the ideal ray picture, the refracted angle is 90°, so the transmitted ray runs along the interface. For incidence beyond the critical angle there is no propagating transmitted ray, although an evanescent electromagnetic field still extends a short distance into the lower-index medium.
Can Snell's law be used for air as n=1?
For many classroom calculations, taking air as n≈1.00 is accurate enough. More precise work can use the actual refractive index of air, which is slightly above 1 and varies with wavelength, temperature, pressure, humidity, and composition.

Formula Explorer connections

Interpretation: This relationship connects light propagation, geometry, wavelength, refraction, interference or image formation. Assumption: Use a consistent sign convention and units. Paraxial rays, thin elements, coherent light, vacuum wavelength or ideal optical components may be assumed.

Telescope Magnification Calculator →Thin Lens Calculator →Young's Double Slit Experiment Calculator →Physics Formula Explorer →