Mini Physics
Part of Mini EducationSwitch subject
Search

Refraction Of Light

Key idea: O Level refraction: explain bending through speed change, use n = sin i/sin r and n = c/v, and track speed, frequency and wavelength.

  • SEC G3 Physics 2027
On this page

Learning objectives

  • Describe wave generation by vibrating sources, ropes and springs
  • Describe ripple-tank waves using wavefronts
  • Explain that waves transfer energy
  • Explain that wave energy transfer does not transfer matter
  • Use amplitude, frequency and wavelength to describe wave motion
  • Define and use wave speed and period and interpret wave graphs
  • Recall and apply wave speed = frequency × wavelength
  • Compare transverse and longitudinal waves and give examples
  • Explain sound production by vibration and the need for a medium
  • Describe sound using compressions and rarefactions
  • Relate sound loudness to amplitude and pitch to frequency
  • Explain reflected-sound echoes and use them to measure distance
  • Explain ultrasound use in sonar and soft-tissue scanning
  • Use the normal, angle of incidence and angle of reflection
  • Apply the law of reflection in constructions, measurements and calculations
  • Use the normal, angle of incidence and angle of refraction
  • Apply sin i divided by sin r as a constant for a fixed pair of media
  • Define refractive index as vacuum light speed divided by medium light speed
  • Explain the critical angle
  • Explain the conditions for total internal reflection
  • Apply total internal reflection to optical fibres and state advantages
  • Describe how a thin converging lens acts on a light beam
  • Define the focal length of a converging lens
  • Construct real and virtual image ray diagrams for a thin converging lens
  • Describe lens images as real or virtual, magnified or diminished, and upright or inverted

1. Definition

A. Refraction of light

Refraction is the change in direction of light when it passes from one transparent medium into another because its speed changes. At normal incidence, speed and wavelength still change at the boundary, but the ray is not deviated.

2. Key Ideas

A. Key terms (must know)

  • Incident ray: incoming ray.
  • Refracted ray: ray after it enters the new medium.
  • Normal: line drawn perpendicular (90°) to the surface at the point of incidence.
  • Angle of incidence, i: angle between incident ray and the normal.
  • Angle of refraction, r: angle between refracted ray and the normal.

B. Laws of refraction (O Level)

  1. The incident ray, refracted ray and normal lie in the same plane.
  2. For a given pair of media, (sin i)/(sin r) = constant

C. Refractive index

The refractive index of a medium, n, is:

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

For light entering from air into a medium, you can also use:

n = (sin i)/(sin r)

D. How the ray bends

  • Into a more optically dense medium (higher n): bends towards the normal.
  • Into a less optically dense medium (lower n): bends away from the normal.
  • If the ray enters along the normal (i = 0°), it does not change direction.

3. Detailed Explanations

A. Why does refraction happen?

At the boundary, one side of the wavefront enters the new medium first and changes speed first. This causes the direction of travel to change (the ray bends).

Refraction, critical angle, and total internal reflectionThree ray diagrams show normal incidence into a higher-index medium, the critical-angle case from higher to lower index, and total internal reflection beyond the critical angle.A: Normal incidenceair, lower nglass, higher ndirection unchangedB: At i = clower nhigher ncr = 90°C: At i > clower nhigher nitotal internal reflection
At normal incidence the ray does not bend, although its speed and wavelength still change. From higher to lower refractive index, the refracted ray reaches the boundary at i = c; total internal reflection occurs only for i > c.

B. No bending at normal incidence

If the incident ray travels along the normal (i = 0°), it slows down or speeds up but does not bend. The speed and wavelength change; only the direction stays unchanged.

C. What happens to speed, frequency and wavelength?

When light enters a different medium:

  • speed changes (that is why refraction happens)
  • frequency f stays the same (set by the source)
  • wavelength λ changes because v = fλ

D. Everyday examples

Bent straw / pencil in water

Light from the submerged part bends away from the normal as it leaves water for air. Your eye traces the emerging rays backwards in straight lines, so the underwater part appears shallower and displaced. The object itself has not bent; the apparent position is an inference from refracted rays.

Observation and explanation

Observation: the submerged section appears shifted. Explanation: rays change speed and direction at the water–air boundary, and the eye assigns them an apparent position along their backward extensions.

Link

Total internal reflection is a special case of refraction: Total Internal Reflection.

4. Common Mistakes

  • Measuring i and r from the surface instead of from the normal.
  • Forgetting to convert degrees-mode on calculator for sin.
  • Using n = c/v but mixing c and v units (both should be m s⁻¹).
  • Writing “denser” to mean “higher mass density” (optical density means higher refractive index).
  • Saying “nothing changes” at normal incidence. The ray is not deviated, but its speed and wavelength still change.

5. Exam Tips

  • Always draw and label the normal first.
  • State the cause: “light changes speed at the boundary”.
  • If asked for a calculation:
    • write the relationship first (n = (sin i)/(sin r) or n = c/v),
    • substitute with units,
    • final answer with sensible rounding.

6. Worked Examples

Modelled example 1

Finding angle of refraction

Core

Problem

Light enters glass from air. The refractive index of glass is n = 1.50 and the incidence angle is 30°. Find the refraction angle.
Study the worked solution

  1. Make the unknown sine term the subject

    Method

    Rearrange n = sin i/sin r to sin r = sin i/n.

    Reason

    The unknown is the angle inside the glass.

    Working

    sin r = (sin 30°)/1.50 = 0.333…

  2. Recover the angle

    Method

    Use inverse sine in degree mode.

    Reason

    The calculator value 0.333… is sin r, not r itself.

    Working

    r = sin⁻¹ (0.333…) ≈ 19.5°

Guided practice 2

Finding refractive index from angles

About 4 min

Problem

A ray goes from air into a liquid. i = 40° and r = 28°. Find the refractive index of the liquid.

Use angles measured from the normal

Hints

Hint 1: select the angle relationship
For air into the liquid, use n = sin i/sin r.
Hint 2: check calculator mode
Evaluate both sines in degrees before dividing.
View solution step by step

  1. Calculate the ratio

    Method

    Divide the sine of incidence by the sine of refraction.

    Reason

    The pair of media is fixed and the ray enters from air.

    Working

    n = (sin 40°)/(sin 28°) ≈ 0.643/0.469 ≈ 1.37

Common misconception 3

Finding speed in a medium

Find and correct the mistake

Learner response

A material has refractive index 1.60. A student multiplies c by n and obtains a speed greater than the vacuum speed. Diagnose the rearrangement and find the correct speed.

Use the physical bound to test the algebra

Unit: m/s

View solution step by step

  1. Rearrange correctly

    Method

    Make medium speed the subject: v = c/n.

    Reason

    A refractive index above 1 means light travels more slowly in the material than in vacuum.

    Working

    v = (3.0 × 10⁸)/1.60

  2. Calculate and check

    Method

    Obtain 1.88 × 10⁸ m s⁻¹.

    Reason

    The result is below c, satisfying the physical bound.

    Working

    v = 1.88 × 10⁸ m s⁻¹

Examiner practice 4

Normal incidence

3 marks

Examination question

Light enters glass from air along the normal, so i = 0°. State the refraction angle and describe what happens to speed, frequency and wavelength. [3 marks]

Separate direction from other wave quantities

View solution step by step

  1. State the direction

    1 mark

    Method

    State r = 0° and no deviation.

    Reason

    Both sides of the wavefront meet the boundary simultaneously at normal incidence.

    Working

    The ray continues along the normal.

  2. Track the wave quantities

    2 marks

    Method

    State that speed decreases in glass, frequency stays constant and wavelength decreases.

    Reason

    The source fixes frequency, while v = fλ links the reduced speed to reduced wavelength.

    Working

    v↓, f unchanged, λ↓.

Challenge 5

Wavelength change in glass

Minimal support

Wave-property transfer

Light in air has wavelength 600 nm and enters glass with refractive index n = 1.50. Find the wavelength in glass and justify the relationship used.

Combine refractive index with unchanged frequency

Hints

Hint 1: compare speeds
In glass, v = c/n.
Hint 2: hold frequency fixed
With v = fλ and unchanged f, wavelength scales with speed.
View solution step by step

  1. Relate the wavelengths

    Method

    Divide the air wavelength by the refractive index.

    Reason

    Glass speed is reduced by factor n, while frequency stays fixed across the boundary.

    Working

    λ_glass = λₐᵢᵣ/n

  2. Calculate the glass wavelength

    Method

    Divide 600 nm by 1.50.

    Reason

    The result should be shorter in the slower medium.

    Working

    λ_glass = 600/1.50 = 400 nm

7. Mind Stretchers

Mind stretcher 1: Toward or away?Extension

A ray travels from water (n ≈ 1.33) into air (n ≈ 1.00). Does it bend toward or away from the normal? Explain.

Show Answer

It bends away from the normal because it is entering a less optically dense medium (lower refractive index), so the speed increases.

Mind stretcher 2: What changes at the boundary?Extension

Light enters a glass block from air. Which quantities definitely change: speed, frequency, wavelength?

Show Answer

Speed changes and wavelength changes. Frequency stays the same (set by the source).

8. Practice and next step

Solve one sine-ratio problem and one n = c/v problem, stating the fixed pair of media and units where applicable. Continue to total internal reflection.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027