Ângulo Crítico em Diamante
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
Formula
diamante → ar
About this calculator
The critical angle calculator for diamond determines the limiting angle for total internal reflection when light travels from diamond to air. Diamond has a high refractive index (n = 2.42), meaning light propagates more slowly in it. The critical angle is the angle of incidence in diamond beyond which light cannot escape into air, being completely reflected internally. This is crucial for understanding the intense brilliance of cut diamonds, as light becomes trapped inside the gem and reflects multiple times before exiting.
The calculation is based on Snell's law, which relates the angles of incidence and refraction to the refractive indices of the media. The formula for the critical angle (θc) is: θc = arcsin(n2 / n1), where n1 is the index of diamond (2.42) and n2 is the index of air (1.00). Thus, the critical angle is approximately 24.4 degrees. Any light ray hitting the diamond-air interface at an angle larger than this will be totally reflected back into the diamond. The calculator performs this computation instantly.
You can use this tool in educational optics contexts, to understand why diamonds are so brilliant, or in jewelry design projects that exploit total internal reflection. It is also useful for students comparing different materials: the higher the refractive index, the smaller the critical angle. For example, ordinary glass (n ≈ 1.5) has a critical angle around 41.8 degrees, much larger than diamond's.
Caution: the calculator assumes the second medium is air (n=1). If another material contacts the diamond (such as water or oil), the critical angle changes. Additionally, diamond's refractive index varies slightly with light color (chromatic dispersion), but the value 2.42 is an average for yellow light (sodium). For precise calculations in optical projects, consider these variations.
Frequently asked questions
What is the critical angle of diamond?
It is the minimum angle of incidence in diamond at which light undergoes total internal reflection when trying to pass into air. For diamond, this angle is approximately 24.4 degrees.
Why does diamond sparkle so much?
Due to its high refractive index (2.42), the critical angle is small, causing light to become trapped inside the gem and reflect internally many times before exiting, producing intense brilliance.
Does the critical angle change if the diamond is immersed in water?
Yes. If diamond is in contact with water (n=1.33), the critical angle increases to about 33.3 degrees because the index difference is smaller.
How do I calculate the critical angle for other materials?
Use the formula θc = arcsin(n2/n1), where n1 is the index of the denser material and n2 of the less dense one. For example, for glass (n=1.5) in air, θc ≈ 41.8°.
Is the refractive index of diamond constant for all colors?
No. Diamond has chromatic dispersion: the index varies with light color. The value 2.42 is for yellow light (589 nm). For blue light, the index is higher; for red, lower.