Refractive Index Converter
Free Refractive index Converter for other units. Enter a value to see equivalent measurements across systems. Includes formulas and worked examples.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Refractive Index Converter
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Formula: n1 x sin(angle1) = n2 x sin(angle2) | Critical angle = arcsin(n2/n1)
Worked example โ Refracted angle = 32.04 degrees (light bends toward normal)
Formula
n1 x sin(angle1) = n2 x sin(angle2) | Critical angle = arcsin(n2/n1)
Snells law relates the incident angle and refracted angle through the refractive indices of two materials. The critical angle for total internal reflection exists only when light travels from a denser to less dense medium (n1 > n2). Light speed in a material = c / n, where c is the speed of light in vacuum.
Worked Examples
Example 1: Light Entering Water from Air
Problem:Light hits water at a 45-degree angle of incidence from air. Find the refracted angle.
Solution:n1 x sin(angle1) = n2 x sin(angle2) 1.000293 x sin(45) = 1.333 x sin(angle2) sin(angle2) = (1.000293 x 0.7071) / 1.333 = 0.5306 angle2 = arcsin(0.5306) = 32.04 degrees
Result:Refracted angle = 32.04 degrees (light bends toward normal)
Example 2: Critical Angle for Glass to Air
Problem:Find the critical angle for total internal reflection from crown glass to air.
Solution:Critical angle = arcsin(n2 / n1) Critical angle = arcsin(1.000293 / 1.523) Critical angle = arcsin(0.6568) Critical angle = 41.04 degrees
Result:Critical angle = 41.04 degrees; angles above this cause total internal reflection
Frequently Asked Questions
What is the refractive index?
The refractive index (n) is a dimensionless number that describes how fast light travels through a material compared to the speed of light in vacuum. It equals the ratio of the speed of light in vacuum (c = 299,792,458 m/s) to the speed of light in the material. For example, water has a refractive index of 1.333, meaning light travels 1.333 times slower in water than in vacuum. The refractive index determines how much light bends when passing between different materials, which is the basis of lenses, prisms, and fiber optics.
What is Snell's law and how does it work?
Snell's law describes the relationship between the angles of incidence and refraction when light passes between two materials with different refractive indices. The formula is n1 x sin(angle1) = n2 x sin(angle2), where n1 and n2 are the refractive indices of the two media, and angle1 and angle2 are measured from the surface normal. When light moves from a less dense to a more dense medium (higher refractive index), it bends toward the normal. When moving to a less dense medium, it bends away from the normal.
What is total internal reflection?
Total internal reflection occurs when light traveling through a denser medium (higher refractive index) hits the boundary with a less dense medium at an angle greater than the critical angle. At this critical angle, the refracted ray travels along the boundary surface. Beyond it, all light is reflected back into the denser medium with no transmission. This phenomenon is the operating principle of fiber optic cables, which trap light inside glass fibers through continuous total internal reflection, allowing data transmission over long distances with minimal loss.
Why does diamond sparkle so much?
Diamond has an exceptionally high refractive index of 2.417, which is among the highest of any natural transparent material. This high refractive index creates a very small critical angle of about 24.4 degrees, meaning total internal reflection occurs easily. Light entering a well-cut diamond bounces internally many times before exiting, creating the characteristic brilliance. Additionally, diamond has high dispersion, meaning it separates white light into spectral colors more than most materials, producing the colorful fire that makes diamonds so prized in jewelry.
References
Reviewed for accuracy by Manoj Kumar, Mathematics Educator ยท Editorial policy
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