Index of Refraction Calculator
Free calculate refractive index from speed of light or using snell's law. calculate angles of refraction.
Input Parameters
Speed of light in vacuum: 299,792,458 m/s
Results
Enter values to calculate
What is Index of Refraction?
The index of refraction (n) is a dimensionless number that describes how much light slows down when passing through a medium compared to its speed in a vacuum.
It's defined as n = c/v, where c is the speed of light in vacuum (299,792,458 m/s) and v is the speed of light in the medium. Higher refractive index means light travels slower in that medium.
Refractive index determines how much light bends (refracts) when entering a different medium, as described by Snell's law. It's fundamental in optics, lens design, fiber optics, and understanding how light interacts with materials.
Index of Refraction Formulas
From Speed
c = speed in vacuum, v = speed in medium
Snell's Law
For calculating n₂ from angles
How to Calculate
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1
Choose calculation method
Use speed method if you know light speed in the medium, or Snell's law if you know angles.
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2
For speed method
Calculate n = c/v, where c = 299,792,458 m/s (speed in vacuum).
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3
For Snell's law
Calculate n₂ = n₁ × sin(θ₁) / sin(θ₂), converting angles to radians if needed.
Practical Examples
Example 1: Water
Light travels at 2.25×10⁸ m/s in water. Calculate the refractive index.
Solution:
n = c / v = 299,792,458 / 225,000,000
n = 1.33 (water's refractive index)
Example 2: Using Snell's Law
Light enters from air (n=1.0003) at 30° and refracts at 20° in a medium. Find the medium's refractive index.
Solution:
n₂ = n₁ × sin(θ₁) / sin(θ₂) = 1.0003 × sin(30°) / sin(20°)
n₂ = 1.46 (could be glass or acrylic)
Applications
Lens Design
Essential for designing lenses, eyeglasses, cameras, and optical instruments to control light bending.
Fiber Optics
Understanding total internal reflection and light propagation in optical fibers for telecommunications.
Gemology
Identifying gemstones and materials based on their unique refractive indices.
Chemistry
Refractometry for measuring solution concentrations and identifying substances.
Frequently Asked Questions
What is the refractive index of common materials?
Vacuum: 1.0, Air: ~1.0003, Water: 1.33, Glass: 1.5-1.9, Diamond: 2.42. Higher values mean light travels slower.
Why does light bend when entering a different medium?
Light changes speed when entering a different medium. The change in speed causes the wavefront to bend, changing direction (refraction).
What is total internal reflection?
When light tries to exit a high-index medium to a lower-index medium at a steep angle, it reflects completely instead of refracting. This occurs when the angle exceeds the critical angle.
Does refractive index depend on wavelength?
Yes! This is called dispersion. Blue light typically has a slightly higher refractive index than red light, causing chromatic aberration in lenses.
Can refractive index be less than 1?
In normal materials, no. But in some metamaterials and plasmas, effective refractive index can be less than 1, allowing unusual optical effects.