Index of Refraction Calculator (Snell's Law)

Apply Snell's law to calculate the refracted angle, index of refraction, or critical angle for total internal reflection when light passes between two media.

REFRACTED ANGLE (θ2)
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Speed Ratio (v1/v2)
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Critical Angle
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Wavelength Ratio
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Deviation Angle
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What Is the Index of Refraction?

The index of refraction (or refractive index) of a material is a dimensionless number that describes how fast light travels through that material relative to its speed in a vacuum. It is defined as n = c/v, where c is the speed of light in vacuum (approximately 3 x 10^8 m/s) and v is the speed of light in the material. A higher refractive index means light travels more slowly through the material.

When light passes from one medium to another with a different refractive index, it changes direction -- a phenomenon called refraction. This bending of light is described by Snell's law, discovered by Willebrord Snell in 1621. Refraction is responsible for many everyday optical effects: the apparent bending of a straw in water, the sparkle of diamonds, mirages, and the operation of lenses and fiber optics.

Snell's Law Formula

n1 × sin(θ1) = n2 × sin(θ2)
θ2 = arcsin( n1 × sin(θ1) / n2 )

Where n1 and n2 are the refractive indices of the two media, and θ1 and θ2 are the angles of incidence and refraction measured from the normal to the surface.

Common Refractive Indices

MaterialRefractive IndexLight Speed (km/s)
Vacuum1.0000299,792
Air1.0003299,702
Water1.333224,901
Crown Glass1.52197,232
Diamond2.417124,034
Silicon3.4287,660

Total Internal Reflection

When light travels from a denser medium (higher n) to a less dense medium (lower n), there exists a critical angle beyond which all light is reflected back into the denser medium. This phenomenon is called total internal reflection (TIR). The critical angle is given by θc = arcsin(n2/n1), and it only exists when n1 > n2.

  • Fiber optics: TIR keeps light trapped inside glass fibers for telecommunications.
  • Prisms: Right-angle prisms use TIR to redirect light in binoculars and periscopes.
  • Diamonds: The high refractive index (2.417) creates a small critical angle (24.4 degrees), causing intense internal reflections that produce brilliance and fire.

Frequently Asked Questions

What happens when the refracted angle would exceed 90 degrees?

When n1 sin(θ1) / n2 exceeds 1, the arcsin function has no solution, meaning refraction cannot occur. Instead, total internal reflection takes place and all light is reflected back into the first medium. This occurs when the angle of incidence exceeds the critical angle.

Does the refractive index depend on wavelength?

Yes. The refractive index varies with the wavelength of light, a phenomenon called dispersion. Blue light has a higher refractive index than red light in most materials. This is why prisms spread white light into a rainbow spectrum, and why chromatic aberration occurs in lenses.

Can the refractive index be less than 1?

For normal materials at optical frequencies, no. However, at X-ray frequencies, many materials have refractive indices slightly less than 1, meaning the phase velocity exceeds the speed of light in vacuum. This does not violate relativity because the group velocity (which carries information) remains below c.