Calculate the angle of refraction using Snell's Law. Includes critical angle, Brewster angle, Fresnel reflectance, and a multi-angle comparison table.
The angle of refraction describes how much a ray of light bends when passing from one transparent medium to another. This bending occurs because light travels at different speeds in different materials, and the change in speed causes the wavefront to pivot at the interface. Snell's Law provides the precise mathematical relationship governing this phenomenon.
When light enters a denser medium (higher refractive index), the refracted ray bends toward the normal, resulting in a smaller angle of refraction compared to the angle of incidence. Conversely, when light passes into a less dense medium, it bends away from the normal. If the angle of incidence exceeds the critical angle in this case, total internal reflection occurs and no refracted ray exists — a principle exploited in fiber optics and prisms.
This calculator applies Snell's Law to compute the angle of refraction for any pair of media and incidence angle. It also provides Fresnel reflectance coefficients, Brewster's angle, critical angle analysis, and a comprehensive multi-angle comparison table to help visualize how refraction changes across the full range of incidence angles.
Whether you're an optics student, lens designer, or photographer, understanding refraction angles is essential. This calculator goes beyond a simple formula solver by providing Fresnel analysis, polarization data, and a multi-angle comparison that would take significant time to compute manually.
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 θ₂ = arcsin((n₁/n₂)·sin(θ₁)). Critical Angle: θ_c = arcsin(n₂/n₁) when n₁ > n₂.
Result: 19.20°
Light from air (n=1.0) entering crown glass (n=1.52) at 30° incidence refracts to arcsin((1.0/1.52)·sin(30°)) ≈ 19.20°.
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This means total internal reflection occurs. No refracted ray exists; all light reflects back into the original medium. This only happens when light moves from a denser to a less dense medium.
Light changes speed at the boundary. Different parts of the wavefront slow down (or speed up) at different times, causing the ray direction to change — similar to a car turning when one wheel hits mud.
No. The refractive index varies with wavelength (dispersion). Blue light typically has a higher refractive index than red, which is why prisms create rainbows.
Lenses use curved refracting surfaces to bend light toward (or away from) the retina, correcting nearsightedness, farsightedness, and astigmatism. Use this as a practical reminder before finalizing the result.
It is the basis for fiber optics, total-internal-reflection prisms in binoculars, and diamond cutting (maximizing internal reflections for brilliance). Keep this note short and outcome-focused for reuse.
Snell's Law applies to any wave at a boundary between media with different propagation speeds. Replace refractive indices with the speed ratio.