Refraction
A short lesson with diagrams, a worked example, a problem to try, and a quick check. Then quiz yourself on 6 practice questions.
Light slows down in materials: n = c/v. When it crosses into a new material at an angle, it bends: n1 sin θ1 = n2 sin θ2 (Snell’s law). Into a higher n, it bends toward the normal; into a lower n, away from it.
1. Snell’s law
2. Total internal reflection
Going from a higher n to a lower n, the light bends away from the normal. At the critical angle θc, the refracted ray skims along the surface (90°).
Beyond θc, no light gets out: it all reflects. That’s how fiber optics carry light around bends.
3. Example, then try it
Light in air enters glass (n = 1.50) at 50° from the normal. Find its angle and speed in the glass.
sin θ2 = (1.00)(sin 50°) ÷ 1.50 = 0.511, so θ2 ≈ 31°.
v = c/n = (3.0 × 10⁸) ÷ 1.50 = 2.0 × 10⁸ m/s.
Light travels up through water (n = 1.33) toward the surface. What happens if it hits the surface at 30° from the normal? What is the critical angle? What happens at 60°?
At 30°: sin θair = 1.33 × sin 30° = 0.665, so it leaves at about 42°, bent away from the normal.
Critical angle: sin θc = 1.00/1.33 = 0.752, so θc ≈ 49°.
At 60°: 1.33 × sin 60° = 1.15, more than 1, so no refracted ray exists. Total internal reflection: all the light reflects back into the water.
Answer: about 42° into the air; θc ≈ 49°; total internal reflection at 60°.
4. Common mistakes
Light passes from air into water at an angle. How does it bend?
Water has a higher index than air, so the light slows down and bends toward the normal.
Ready to practice?
6 questions on Refraction, each with a hint and an explanation for every wrong answer.