About the Angle of Incidence
The angle of incidence is the angle between an incoming ray — light, or any wave — and the normal: the imaginary line drawn perpendicular to a surface at the point where the ray meets it. It is always measured from the normal, never from the surface itself. When that ray crosses from one transparent medium into another (say, from air into water), part of it reflects and part of it refracts, or bends. Both behaviors follow exact, well-established laws.
Snell's Law: finding the angle of refraction
Snell's Law relates the angle of incidence θ₁ and angle of refraction θ₂ to the refractive indices n₁ and n₂ of the two media:
n₁ sin(θ₁) = n₂ sin(θ₂)
Solved for the refraction angle: θ₂ = arcsin[(n₁/n₂) × sin(θ₁)]. This calculator evaluates that formula directly from your three inputs.
The law of reflection
Separately from refraction, some light always reflects off the boundary. The law of reflection states that the angle of reflection is always exactly equal to the angle of incidence, with both measured from the normal on the same side of the boundary and within the same medium (n₁). This holds no matter what n₂ is.
The critical angle and total internal reflection
When light travels from a denser medium into a less dense one (n₁ > n₂), Snell's Law predicts a critical angle, θc = arcsin(n₂/n₁). At incidence angles beyond θc, the equation for sin(θ₂) exceeds 1 — a value with no real solution — so no refracted ray exists at all. Instead, total internal reflection occurs and all the light bounces back into the first medium. This effect is what keeps light trapped inside optical fibers and creates the shimmering total-reflection edge seen underwater near the surface.
Typical refractive indices
- Vacuum: n = 1 (exact, by definition)
- Air: n ≈ 1.0003 (often rounded to 1.00)
- Water: n ≈ 1.33
- Crown glass: n ≈ 1.52
- Diamond: n ≈ 2.42
Reading your results
A higher n₂ relative to n₁ bends the ray closer to the normal (θ₂ < θ₁); a lower n₂ bends it farther away. If n₁ < n₂, total internal reflection can never happen, so the critical angle result shows "N/A." Always keep angles in degrees measured from the normal, and remember that refractive index itself has no units.