Snells Law Calculator
Our optics & light calculator computes snells law accurately. Enter measurements for results with formulas and error analysis.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
n1 sin(theta1) = n2 sin(theta2)
Where n1 and n2 are the refractive indices of the two media, theta1 is the angle of incidence, and theta2 is the angle of refraction. Both angles are measured from the normal (perpendicular) to the interface surface.
Worked Examples
Example 1: Light Entering Glass from Air
Problem:A beam of light hits a glass surface (n=1.52) at 45 degrees from air (n=1.0). Find the refraction angle.
Solution:Apply Snell's law: n1 sin(theta1) = n2 sin(theta2)\n1.0 x sin(45) = 1.52 x sin(theta2)\n0.7071 = 1.52 x sin(theta2)\nsin(theta2) = 0.7071 / 1.52 = 0.4652\ntheta2 = arcsin(0.4652) = 27.71 degrees\nBrewster's angle = arctan(1.52/1.0) = 56.66 degrees
Result:Refraction Angle: 27.71 degrees (light bends toward normal entering denser medium)
Example 2: Total Internal Reflection in Glass
Problem:Light travels inside glass (n=1.5) toward an air boundary (n=1.0). What is the critical angle?
Solution:Critical angle = arcsin(n2/n1) = arcsin(1.0/1.5)\n= arcsin(0.6667) = 41.81 degrees\nAny angle of incidence above 41.81 degrees will cause total internal reflection.\nAt exactly 41.81 degrees, the refracted ray grazes along the surface at 90 degrees.
Result:Critical Angle: 41.81 degrees | Above this angle, 100% of light is reflected
Frequently Asked Questions
What is Snell's law and what does it describe in optics?
Snell's law describes how light bends (refracts) when it passes from one medium into another with a different refractive index. The law states that the product of the refractive index and the sine of the angle of incidence in one medium equals the product of the refractive index and the sine of the refraction angle in the second medium (n1 sin theta1 = n2 sin theta2). This fundamental principle was first accurately described by Willebrord Snellius in 1621 and independently by Rene Descartes. It applies to all types of waves including light, sound, and water waves whenever they cross a boundary between media with different propagation speeds.
How do anti-reflection coatings work using principles from Snell's law?
Anti-reflection (AR) coatings reduce unwanted reflections by applying thin film layers with specific refractive indices and thicknesses to optical surfaces. A single-layer AR coating works best when its refractive index equals the square root of the product of the two surrounding media indices, and its thickness is one-quarter of the wavelength in the coating material. This creates destructive interference between reflections from the top and bottom surfaces of the coating. Multi-layer coatings stack several thin films to achieve broadband anti-reflection across a wide wavelength range. Modern smartphone screens, camera lenses, and solar panels all use AR coatings to improve light transmission and reduce glare.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy