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 by Manoj Kumar, Mathematics Educator
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)\n1.000293 x sin(45) = 1.333 x sin(angle2)\nsin(angle2) = (1.000293 x 0.7071) / 1.333 = 0.5306\nangle2 = 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)\nCritical angle = arcsin(1.000293 / 1.523)\nCritical angle = arcsin(0.6568)\nCritical 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.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy