Critical Angle Calculator
Only exists going from dense to less dense.
Work out Critical Angle. Only exists going from dense to less dense. Free, with no account and nothing to install.
Critical angle
48.626°
Below the critical angle of 48.63°, so the light refracts and crosses the boundary.
Snell's law says n₁ sin θ₁ = n₂ sin θ₂. When light moves into a less dense medium the refracted angle exceeds the incident one, and at some incidence the refracted ray would need to exceed 90° — which it cannot, so all of the light reflects back instead. That angle is the critical angle, and it exists only going from denser to less dense. Going the other way there is no angle at which light fails to cross, which is why this reports "none" rather than a number when you pick that direction. Total internal reflection is what makes optical fibre work: light entering within the acceptance cone bounces along the core indefinitely, losing almost nothing at each reflection. It is also why diamond sparkles — a critical angle of about 24° means light entering the top has to bounce several times before it can find a way out.
How the Critical Angle Calculator works
The critical angle for total internal reflection between two media, and where a ray at a given incidence actually goes. A critical angle only exists going from the denser medium to the less dense one.
Also known as: total internal reflection angle · critical angle water to air · why does diamond sparkle · snells law refraction angle
Frequently asked questions
What is the critical angle?
The angle of incidence beyond which light cannot cross into a less dense medium and reflects entirely instead. For water to air it is about 48.6°; for diamond to air, about 24°.
Why is there no critical angle going the other way?
Because entering a denser medium bends light toward the normal, so there is no incidence at which the refracted ray would exceed 90°. Light always crosses, which is why this reports "none" rather than a number.
How does optical fibre work?
Total internal reflection. Light entering within the acceptance cone bounces along the core indefinitely, losing almost nothing at each reflection — which is what makes long-distance data transmission possible.
Why does diamond sparkle?
Its refractive index of 2.42 gives a critical angle of only 24°, so light entering the top bounces several times inside before it can find a way out. Cutters shape the facets specifically to exploit that.
What is Snell's law?
n₁ sin θ₁ = n₂ sin θ₂. The critical angle is what you get by setting the refracted angle to 90° and solving for the incidence.
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