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Physics · 4. Waves and optics

Refraction and Snell’s law

Measure incidence and refraction angles and determine refractive index from evidence.

40 minutesContent version: 2.1
Start the interactive pathwayOpen the virtual experiment

Driving question

Can a transparent material be identified solely from the path of a light ray?

Curriculum coverage

Vietnam 2018 and Cambridge: refraction, refractive index and total internal reflection.

Model scope and limitations

Homogeneous transparent media; neglects dispersion unless wavelength is varied.

Learning objectives

  • Apply n₁sinθ₁ = n₂sinθ₂.
  • Measure angles from normal, not interface.
  • Use sinθ₁–sinθ₂ graph to determine refractive index.

Prerequisite knowledge

  • Sine function and angular measurement.
  • Incident ray, normal, refracted ray.

Core knowledge

Snell’s law

n₁sinθ₁ = n₂sinθ₂, both angles measured from the normal.

Bending direction

Light bends toward the normal when entering a denser optical medium.

Total internal reflection

Occurs only from denser to rarer medium when incidence exceeds critical angle sin(ic) = n₂/n₁.

Worked example

From air into glass n = 1.50 at 30° incidence: sin r = sin 30° / 1.50 = 0.333, so r ≈ 19.5°.

Misconceptions to avoid

  • Incidence and refraction angles are measured from the normal, not the boundary surface.
  • Total internal reflection only occurs when light travels from higher to lower optical density.

Virtual experiment procedure: Snell’s law of refraction

  1. Select two media and record their refractive indices.
  2. Vary incidence angle from 10° to 60°, recording refraction angle.
  3. Compute sines of both angles and verify ratio or graph gradient.

Safety and cautions

  • Never look directly into laser beams in real laboratories.

Evidence to collect

  • A table of i, r, sin i and sin r for at least five incidence angles.
  • A plot of sin i versus sin r with refractive index deduced from slope.
Open the virtual experiment
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Diagnostic check

1. Incidence and refraction angles are measured relative to what?

  1. The normal
  2. The interface
  3. The reflected ray
Show answer and explanation

Correct answer: The normal

All angles in geometrical optics are measured from the normal.

2. When light travels from air into water, how does the refracted ray bend?

  1. Bends toward the normal
  2. Bends away from the normal
  3. Continues straight without bending
Show answer and explanation

Correct answer: Bends toward the normal

Water has higher refractive index, so r < i, bending toward normal.

Application practice

1. Light passes from air (n=1) into water (n=1.33) at 45° incidence. sin(r)?

  1. 0.532
  2. 0.707
  3. 0.940
Show answer and explanation

Correct answer: 0.532

sin(r) = sin(45°)/1.33 = 0.707 / 1.33 ≈ 0.532.

2. What are the conditions for total internal reflection?

  1. Denser to rarer medium with i > ic
  2. Rarer to denser medium
  3. Incidence angle always 90°
Show answer and explanation

Correct answer: Denser to rarer medium with i > ic

Requires n₁ > n₂ and incidence angle exceeding critical angle ic; at i = ic, the refracted ray travels along the boundary.

3. Critical angle from glass (n=1.5) to air (n=1)?

  1. approx 41.8°
  2. approx 60°
  3. approx 30°
Show answer and explanation

Correct answer: approx 41.8°

sin(ic) = 1/1.5 = 0.667 ⇒ ic ≈ 41.8°.

Academic references

  1. Cambridge IGCSE Physics 0625 — official syllabus and resources
  2. Cambridge AS & A Level Physics 9702 — official syllabus
  3. OpenStax Physics — peer-reviewed high-school physics
  4. BIPM — SI Brochure, 9th edition

This lesson is maintained against the cited sources below. Simulations are learning models and do not replace supervised physical-laboratory safety procedures.

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