Snell's Law describes how light (or any wave) bends when it crosses the boundary between two media with different refractive indices. The law states: n1 times sin(theta1) equals n2 times sin(theta2), where n1 and n2 are the refractive indices of the two media, and theta1 and theta2 are the angles of incidence and refraction measured from the normal to the surface. A higher refractive index means a slower wave speed in that medium.

What is total internal reflection?

Total internal reflection (TIR) occurs when light tries to pass from a denser medium (higher refractive index) to a less dense medium (lower refractive index) at an angle of incidence greater than the critical angle. At the critical angle, the refracted ray runs along the surface (theta2 = 90 degrees). Beyond this angle, no refracted ray exists and all the light is reflected back into the denser medium. TIR is the principle behind optical fibres.

What is the refractive index of glass?

Common glass (crown glass) has a refractive index of about 1.52, meaning light travels about 1.52 times slower in glass than in a vacuum. Flint glass is about 1.62. Diamond has one of the highest refractive indices for transparent materials at about 2.42, which is why diamonds sparkle so intensely (TIR occurs within the stone at many angles). The refractive index of water is about 1.33 and of air is approximately 1.0003, usually taken as 1.

Snell's Law Calculator

When a wave, whether it is light, sound, or any other type, crosses the boundary between two media with different wave speeds, it bends. This bending is called refraction, and its rules are governed by Snell's Law, which states that n1 times the sine of the angle of incidence equals n2 times the sine of the angle of refraction, where n1 and n2 are the refractive indices of the two media and the angles are measured from the normal to the surface (a line perpendicular to the boundary). A refractive index is a dimensionless number that tells you how much slower light travels in a material compared with a vacuum. Air has a refractive index of approximately 1, water is about 1.33, and standard glass is about 1.52. Light bends toward the normal when it enters a denser medium (higher n) and away from the normal when it exits into a less dense medium. When moving from denser to less dense, there is a special angle called the critical angle at which the refracted ray lies exactly along the surface. Beyond this angle, no light can cross the boundary and all of it reflects back: total internal reflection. This principle is what makes optical fibres work, allowing light to travel around bends without leaking out. This calculator solves Snell's Law for the refracted angle, calculates the critical angle (if the geometry allows for total internal reflection), and tells you whether total internal reflection is occurring. Common material presets are provided for the refractive indices.

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Medium 1 preset

Refractive index n1 (medium 1)

Angle of incidence θ1

Medium 2 preset

Refractive index n2 (medium 2)

19.47°

angle of refraction θ2

Critical angleN/A (n1<n2)

TIR occurring?No

Speed ratio v1/v21.500

n1 sin θ10.5000

Angles are measured from the normal to the surface. TIR only occurs when light travels from higher-n to lower-n medium above the critical angle.

How it works

Snell's Law: n1 × sin(θ1) = n2 × sin(θ2). Rearranging: sin(θ2) = n1 sin(θ1) / n2; then θ2 = arcsin(n1 sin(θ1) / n2). If the quantity n1 sin(θ1) / n2 exceeds 1, total internal reflection occurs and no refracted ray exists. Critical angle θ_c = arcsin(n2/n1) when n1 > n2; this angle only exists when going from a denser to a less dense medium. Speed ratio v1/v2 = n2/n1.

Worked example

Light travels through air (n1 = 1.0) and strikes a glass surface (n2 = 1.5) at an angle of incidence θ1 = 30 °. Using Snell's Law: sin(θ2) = 1.0 × sin(30°) / 1.5 = 0.5 / 1.5 = 0.3333. So θ2 = arcsin(0.3333) = 19.47 °. The light bends toward the normal as expected. The critical angle for this glass-to-air interface (n1=1.5, n2=1) is arcsin(1/1.5) = 41.81 °. These match the default values pre-filled above.

Related calculators

Wave Speed Calculator: find wave speed, frequency, or wavelength using v = f lambda.
Doppler Effect Calculator: calculate observed frequency shift for moving sources.
Percent Error Calculator: compare a measured angle of refraction to a theoretical value.
Measurement Uncertainty Calculator: quantify uncertainty in an experimental angle measurement.

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