Calculate the angle of incidence using Snell's Law given refractive indices and angle of refraction. Includes Fresnel reflectance and Brewster angle.
The angle of incidence is the angle between an incoming light ray and the normal (perpendicular line) to the surface at the point of contact. This fundamental concept in optics governs how light behaves when it encounters a boundary between two different media. Understanding the angle of incidence is crucial for designing optical systems, fiber optics, lenses, and many photonic devices.
When a ray of light strikes a surface separating two transparent media, part of the light is reflected and part is refracted (bent). The relationship between the angle of incidence and the angle of refraction is described by Snell's Law: n₁ sin(θ₁) = n₂ sin(θ₂), where n₁ and n₂ are the refractive indices of the two media and θ₁ and θ₂ are the angles of incidence and refraction respectively.
This calculator not only computes the angle of incidence from a known refraction angle but also provides critical additional information such as Brewster's angle (where reflected light becomes perfectly polarized), Fresnel reflectance coefficients for both s-polarized and p-polarized light, total internal reflection conditions, and a comprehensive material comparison table showing how different media affect the angle of incidence.
This calculator is essential for optics students, engineers, and anyone working with light at interfaces between different media. It instantly solves Snell's Law in reverse and provides Fresnel reflectance data, Brewster's angle, and material comparisons that would otherwise require multiple separate calculations.
This tool is designed for quick, accurate results without manual computation. Whether you are a student working through coursework, a professional verifying a result, or an educator preparing examples, accurate answers are always just a few keystrokes away.
Snell's Law: n₁ · sin(θ₁) = n₂ · sin(θ₂), so θ₁ = arcsin((n₂ / n₁) · sin(θ₂)). Brewster's Angle: θ_B = arctan(n₂ / n₁). Critical Angle (when n₁ > n₂): θ_c = arcsin(n₂ / n₁).
Result: 30.87°
With light traveling from air (n=1.0) into glass (n=1.5) with a refraction angle of 20°, the angle of incidence is arcsin((1.5/1.0)·sin(20°)) ≈ 30.87°.
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The angle of incidence is the angle between an incoming ray of light and the normal (perpendicular) to the surface at the point where the ray strikes the surface. Use this as a practical reminder before finalizing the result.
They are related by Snell's Law: n₁·sin(θ₁) = n₂·sin(θ₂). When light passes from a less dense to a denser medium, the angle of incidence is larger than the angle of refraction.
When light travels from a denser medium to a less dense one (n₁ > n₂), there exists a critical angle beyond which all light is reflected back. This is the principle behind fiber optics.
Brewster's angle is the angle of incidence at which reflected light is completely polarized. It equals arctan(n₂/n₁) and is used in laser windows and polarizing optics.
Fiber optics rely on total internal reflection. The angle of incidence must exceed the critical angle so that light bounces along the fiber without escaping.
The angle of incidence itself is geometric, but the refractive index varies with wavelength (dispersion), which changes how light bends at a given incidence angle. Keep this note short and outcome-focused for reuse.