4PH1

Reflection & Refraction

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Practise

Exam Frequency Analysis

Past paper frequency (2018 to 2024)

This topic accounts for approximately 9% of your exam marks.

stable
Medium
Stable9%

Ray diagrams, Snell's Law and critical angle calculations appear regularly.

The refractive index

  • The (n) of a material is the ratio of the speed of light in a vacuum to the speed of light in the material:

n = (speed of light in a vacuum) / (speed of light in the medium)

  • A few key facts about n:
    • Light always travels slower in matter than in a vacuum, so n is always greater than 1
    • The higher the refractive index, the slower light moves through the material and the more the ray bends when it enters
    • Refractive index is a ratio of two speeds, so it has no units
  • Typical values for common materials:
    • air ≈ 1.00 (effectively the same as vacuum)
    • water ≈ 1.33
    • perspex / acrylic ≈ 1.49
    • crown glass ≈ 1.50
    • diamond ≈ 2.42 (one of the largest of any everyday material, which is why cut diamonds sparkle so brightly)

Snell's law

n = sin i / sin r

  • where:
    • n = refractive index of the second medium (taking the first medium as air, where n ≈ 1)
    • i = angle of incidence in air (measured from the normal)
    • r = angle of refraction in the denser medium (measured from the normal)
  • Important details:
    • sin i / sin r is not the same as i / r; never just cancel the "sin"
    • When solving for r, find sin r first, then take sin⁻¹ to get the angle
Worked example

Using n = sin i / sin r

Light passes from air into glass of refractive index 1.5, meeting the surface at an angle of incidence of 30°. Calculate the angle of refraction.

Solution:

  • Rearrange n = sin i / sin r to make sin r the subject: sin r = sin i ÷ n
  • Substitute, taking the sine of the angle first: sin r = sin 30° ÷ 1.5 = 0.5 ÷ 1.5 = 0.333
  • Take the inverse sine to find the angle: r = sin⁻¹(0.333) = 19.5°

Take the sine of each angle before dividing — the mark scheme rejects dividing the angles directly (30 ÷ 1.5 = 20° is wrong). Never treat "sin" as a multiplier that can be cancelled.

Example A — a ray of light hits a glass block (n = 1.50) at an angle of 30° to the normal. Calculate the angle of refraction inside the glass.

  • Rearrange Snell's law: sin r = sin i / n
  • sin r = sin 30° / 1.50 = 0.500 / 1.50 = 0.333
  • r = sin⁻¹(0.333) = 19.5°

Example B — a light ray enters a water tank from air. The angle of refraction inside the water is 22°. The refractive index of the water is 1.33. Calculate the angle of incidence.

  • Rearrange Snell's law: sin i = n × sin r
  • sin i = 1.33 × sin 22° = 1.33 × 0.3746 = 0.4982
  • i = sin⁻¹(0.4982) = 29.9°