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Waves & Optics Formula

What is Snell's Law of Refraction?

Light bends when it crosses an interface between media of different optical densities.

Formula: n_1\sin\theta_1 = n_2\sin\theta_2

Plain-English Meaning

When light moves from air into water (or glass), it bends. The bending follows a simple rule — Snell's law — that involves refractive index n (how much the medium slows light) and angle from the perpendicular (normal). Total internal reflection happens when light tries to escape at too steep an angle.

If a waves question feels messy, sketch the geometry or phase relationship first, then return to the algebra.

Deeper Explanation

n = c/v (refractive index). Snell's law: n₁ sinθ₁ = n₂ sinθ₂ (angle measured from normal). Critical angle: θ_c = arcsin(n₂/n₁) — beyond this, total internal reflection occurs. Applies to all waves; for sound, n = c₁/c₂.

Worked Example

Problem: Light travels from water (n=1.33) to glass (n=1.5) at 45°. Find refracted angle.

  • n₁ sinθ₁ = n₂ sinθ₂
  • 1.33 × sin45° = 1.5 × sinθ₂
  • sinθ₂ = 1.33 × 0.7071 / 1.5 = 0.9404/1.5 = 0.627
  • θ₂ = arcsin(0.627) ≈ 38.8°

Result: θ₂ ≈ 38.8° (light bends toward normal as it enters denser glass)

At A Glance

Category: Waves & Optics

Levels covered: High School, College, Masters, PhD

Best use: Start with the formula meaning, then move to the worked example and quiz so the equation turns into a tool instead of a memorised line.