Lesson 2 of 5The Wave Nature of Light

Unit 4 · Lesson 2 of 5

Huygens' Principle and the Particle-vs-Wave Debate

Newton's particles against Huygens' waves: how wavelets explain reflection and refraction, why the two models disagreed about the speed of light in water, and the experiments from Young to Maxwell that settled the argument in favour of waves, at least until the photon arrived.

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Key things to remember

1Huygens' principle: every point on a wavefront is a source of wavelets moving at the wave speed; the new wavefront is the line tangent to all the wavelets.
2Snell's law in wave form: $\frac{sin θ _{1}}{sin θ _{2}} = \frac{v _{1}}{v _{2}} = \frac{λ _{1}}{λ _{2}} = \frac{n _{2}}{n _{1}} .$
3Crossing a boundary changes a wave's speed and wavelength but not its frequency; in a medium of index $n$ , $v = c / n$ and $λ = λ_{v a c uu m} / n$ .
4Newton's particle model predicted light is faster in water; the wave model predicted slower. Foucault (1850) found it slower.
5Key evidence for waves: Young's interference (1801 to 1803), the Poisson–Arago spot (1818 to 1819), Foucault's speed in water (1850), Maxwell's electromagnetic waves (1860s).

What is light? In the late 1600s two of the greatest scientists alive gave opposite answers. Isaac Newton argued that light is a stream of tiny, fast particles, which he called corpuscles. Christiaan Huygens, a Dutch physicist, argued that light is a wave spreading through space, like sound or ripples on a pond. Both models explained the everyday facts: light travels in straight lines, it reflects off mirrors, and it bends when it enters water. So how do you choose between two models that both seem to work? You look for a situation where they make different predictions and then test it. That search took about 150 years, and it is a model of how science settles an argument.

Two models of light

ANewton's corpuscular (particle) model

Straight-line travel and sharp shadows: particles move in straight lines unless a force acts
Reflection: particles bounce off a surface like perfectly elastic balls, so the angles are equal
Refraction: the denser medium attracts the particles, adding to the velocity component perpendicular to the surface, so light should go faster in water
Colours: different particles for different colours
Diffraction: no interference fringes expected; the faint edge effects already seen were blamed on forces from the edge

BHuygens' wave model

Straight-line travel: wavefronts advance steadily in the direction they face
Reflection: each point of the wavefront reflects in turn, giving equal angles
Refraction: waves slow down in the denser medium and the wavefront pivots, so light should go slower in water
Colours: later explained as different wavelengths
Diffraction: a small bending into shadows should occur if the wavelength is small

Huygens' principle: every point is a new source

Huygens' great idea was a way to predict where a wavefront will be next. Treat every point on a wavefront as a tiny source of circular wavelets that spread forward at the wave's speed. After a short time, draw the line that just touches the fronts of all those wavelets (their common tangent, or envelope). That line is the new wavefront. For a straight wavefront in open space, the wavelets combine into another straight wavefront a little farther on, so the wave travels in a straight line. Apply the same rule at a mirror and reflection falls out. A wavefront striking a mirror at an angle reaches one end first, so that end starts its reflected wavelet earlier. By the time the far end arrives, the first wavelet has grown to exactly the distance the far end travelled, and the two right triangles formed are congruent. The reflected wavefront therefore leaves at the same angle it arrived: $θ_{i} = θ_{r}$ . You met the same principle in Interference and Diffraction of Waves, where it explained why waves bend around the edges of a gap.

Refraction with wavelets: Snell's law in wave form

Now let a straight wavefront cross a boundary at an angle into a medium where the wave is slower. Call the length of boundary the wavefront spans $A B$ . The end at $A$ touches the boundary first and starts a wavelet in the slow medium. During the time $t$ the other end takes to travel $v_{1} t$ and reach $B$ , the wavelet from $A$ grows only to radius $v_{2} t$ . The new wavefront, drawn from $B$ tangent to that smaller wavelet, is tilted closer to the boundary, so the ray bends toward the normal. From the two right triangles, $sin θ_{1} = v_{1} t / A B$ and $sin θ_{2} = v_{2} t / A B$ . Dividing cancels $t$ and $A B$ .

\frac{sin θ _{1}}{sin θ _{2}} = \frac{v _{1}}{v _{2}} = \frac{λ _{1}}{λ _{2}} = \frac{n _{2}}{n _{1}} n = \frac{c}{v}

Snell's law in wave form. Equivalently n1 over n2 equals v2 over v1 equals lambda 2 over lambda 1. The bending happens because the speed changes.

Frequency stays fixed; wavelength changes

Each wavelet is started by the wave arriving at the boundary, so the wave on both sides oscillates at the same rate: the frequency does not change when a wave crosses into a new medium. Since

v = f λ

with

f

fixed, the wavelength changes in proportion to the speed. Red light of

633 nm

in air is still red light in water, but its wavelength there is only

633/1.33 = 476 nm

Loading interactive…

Change the frequency and wave speed and watch the wavelength respond. At a boundary the frequency is held fixed, so a slower medium means a shorter wavelength.

The deciding evidence

The two models made opposite predictions about refraction. Newton's particles had to speed up in water; Huygens' waves had to slow down. In 1690 no one could measure the speed of light in a tank of water, so the argument was settled by reputation instead, and Newton's reputation was enormous. Through the 1700s most physicists accepted particles. The wave model's revival began with Thomas Young's two-slit interference pattern, which you will analyse in the next lesson, and it was completed when Léon Foucault, in 1850, used a rapidly rotating mirror to time light over a short path and found that it travels more slowly in water than in air, just as Huygens' model required. Meanwhile, polarization experiments showed that light waves must be transverse, not longitudinal like sound, and in the 1860s James Clerk Maxwell's equations predicted electromagnetic waves travelling at exactly the measured speed of light.

Date	Evidence	Why it favoured waves
1690	Huygens publishes his Treatise on Light	Wavelets explain reflection and refraction, predicting slower light in denser media
1801 to 1803	Young's double-slit experiment	Light plus light can make darkness: only waves interfere
1818 to 1819	Fresnel's diffraction theory and the Poisson–Arago spot	A bright spot appears in the centre of a round shadow, exactly as wave theory predicts
1850	Foucault measures light in water	Light is slower in water, contradicting the particle model's prediction
1860s	Maxwell's electromagnetic theory	Changing electric and magnetic fields form a wave that travels at the speed of light
1887 to 1888	Hertz produces and detects radio waves	Confirms that electromagnetic waves exist and behave like light

Fig 1Interference: waves in phase add and waves half a wavelength out of step cancel. Young's dark fringes are places where light waves cancel, which particles cannot do.

Poisson's objection becomes the proof

When Augustin Fresnel entered his wave theory of diffraction in an 1818 competition of the French Academy of Sciences, the mathematician Siméon Poisson, a supporter of particles, pointed out what he took to be an absurd consequence. Light waves diffracting around the edge of a round disc would all travel the same distance to the centre of the shadow and arrive in phase, so there should be a bright spot in the middle of the shadow. François Arago did the experiment and found the spot. It is now called the Poisson spot or Arago spot, and Fresnel won the prize.

The story does not end here

By 1900 the wave model looked complete. Then the photoelectric effect, which you will meet in Unit 5, showed that light also arrives in particle-like packets called photons. Modern physics keeps both pictures: light travels and interferes as a wave, and it delivers energy as particles. Newton was not simply wrong; his particle model was answering a question nobody yet knew how to ask.

Worked examples

Reveal one step at a time and try to beat it to the next line.

Example 1

Yellow sodium light has a wavelength of

589 nm

in air. Find its frequency, and its speed and wavelength in water (

n = 1.33

Example 2

Light in air strikes a glass surface at

4 0^{\circ}

to the normal. Light travels at

2.00 \times 1 0^{8} m/s

in this glass. Use the wave form of Snell's law to find the angle of refraction and the glass's refractive index.

Example 3

In a ripple tank, water waves of wavelength

2.0 cm

travel at

24 cm/s

in deep water. They cross into shallow water, hitting the boundary at

3 0^{\circ}

and refracting to

2 0^{\circ}

. Find the frequency, and the speed and wavelength in the shallow water.

Example 4

Light passes from air into water, with an angle of incidence of

5 0^{\circ}

and an angle of refraction of

3 5^{\circ}

. What speed of light in water does each model predict, and which agrees with Foucault's measurement?

Where marks get lost

Thinking the frequency changes when light enters a new medium. The frequency is set by the source; only the speed and the wavelength change.
Writing Snell's law upside down in speed form. The larger angle goes with the larger speed: $sin θ_{1} / sin θ_{2} = v_{1} / v_{2}$ , but $= n_{2} / n_{1}$ for indices.
Saying Newton's model failed to explain refraction. It explained the bending well; it failed because it predicted the wrong speed in water.
Treating Huygens' wavelets as separate waves you could see. They are a construction: only their common tangent, the new wavefront, is observed.
Assuming the wave model is the final word. Light also behaves as particles (photons), so both models capture part of the truth.

Flashcards 8

Huygens' principle

Corpuscular model

Wave model's prediction for water

Snell's law, wave form

+ 4 more

Practice

Diamond has a refractive index of

2.42

. What is the speed of light in diamond, in units of

1 0^{8} m/s

? Give three significant figures.

× 10⁸ m/s

Red laser light has a wavelength of

633 nm

in air. What is its wavelength in water (

n = 1.33

), in nanometres? Give three significant figures.

Water waves travelling at

30 cm/s

meet the boundary of a shallow region at an angle of incidence of

5 0^{\circ}

. In the shallow region they travel at

20 cm/s

. What is the angle of refraction, in degrees? Give three significant figures.

Light of wavelength

600 nm

in air has a wavelength of

400 nm

inside a piece of plastic. What is the plastic's refractive index? Give three significant figures.

What did Newton's corpuscular model predict about the speed of light in water compared with air?

What did Arago observe when he shone light past a small round disc?

When a light wave passes from air into glass, which quantity stays the same?

Which principle says that every point on a wavefront acts as a source of new wavelets? Give its name.

Put these milestones in the particle-versus-wave debate in chronological order.

1Maxwell predicts electromagnetic waves
2Foucault measures the speed of light in water
3Hertz produces and detects radio waves
4Huygens publishes his wave theory of light
5Young's double-slit experiment
6Arago observes the bright spot in a disc's shadow

Match each observation to the conclusion it supports.

Dark fringes between two lit slits

Light is slower in water than in air

Bright spot in a round shadow

Electromagnetic waves travel at the measured speed of light

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