Snell's Law & Refraction Simulator — Bend Light Between Media

simulator beginner ~8 min
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θ₂ = 19.5° — Light bends toward the normal when entering a denser medium (n₁=1.0 → n₂=1.5).

Light entering glass (n=1.5) from air (n=1.0) at 30° refracts to 19.5°, bending toward the normal as it slows down in the denser medium.

Formula

n₁ sin(θ₁) = n₂ sin(θ₂)
θ_c = arcsin(n₂/n₁)
n = c/v

Refraction: Light Bending at Boundaries

When light crosses the boundary between two transparent materials — say, from air into glass — it changes direction. This bending, called refraction, occurs because light travels at different speeds in different media. In a vacuum, light moves at c = 3×10⁸ m/s, but in glass it slows to roughly 2×10⁸ m/s. The refractive index n = c/v quantifies this slowdown. Snell's Law, n₁ sin(θ₁) = n₂ sin(θ₂), precisely predicts how much the light bends based on the refractive indices and the angle of incidence.

Total Internal Reflection

When light travels from a denser medium (higher n) to a less dense one, it bends away from the normal. At a specific angle — the critical angle θ_c = arcsin(n₂/n₁) — the refracted ray grazes the surface at 90°. Beyond this angle, something dramatic happens: no light passes through the boundary at all. It is completely reflected back, like a perfect mirror. This total internal reflection is not just a curiosity; it is the principle that makes fiber optic communications possible, carrying internet traffic around the world at the speed of light.

Dispersion and Color

The refractive index actually depends on wavelength — a phenomenon called dispersion. Blue light bends more than red because glass has a slightly higher refractive index at shorter wavelengths. This is why a prism splits white light into a rainbow spectrum, and why the edges of lenses can show chromatic aberration. Newton's famous prism experiment in 1666 demonstrated that white light is composed of all visible colors, each refracted by a different amount through the glass.

Applications in Modern Technology

Refraction is the foundation of lens design — from eyeglasses correcting vision to telescope objectives gathering starlight. Camera lenses use multiple glass elements with carefully chosen refractive indices to minimize aberrations and produce sharp images. Anti-reflection coatings exploit thin-film interference to reduce unwanted reflections at lens surfaces. Understanding and controlling refraction remains central to optical engineering, from smartphone cameras to laser surgery to the fiber networks carrying global communications.

FAQ

What is Snell's Law?

Snell's Law relates the angles of incidence and refraction when light passes between media: n₁ sin(θ₁) = n₂ sin(θ₂). Light bends toward the normal when entering a denser medium (higher n) and away from the normal when entering a less dense medium.

What is total internal reflection?

When light travels from a denser medium to a less dense one (n₁ > n₂) at an angle exceeding the critical angle θ_c = arcsin(n₂/n₁), all light reflects back — none enters the second medium. This is the principle behind fiber optic cables.

Why do diamonds sparkle so brilliantly?

Diamond has an extremely high refractive index (2.42), creating a small critical angle of about 24.4°. Most light entering a well-cut diamond undergoes total internal reflection multiple times before exiting, producing intense brilliance and fire.

What causes a rainbow?

Rainbows form through refraction and reflection inside water droplets. White light enters a droplet, refracts (separating into colors due to dispersion), reflects off the back surface, and refracts again on exit — each wavelength emerging at a slightly different angle.

Sources

Embed

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