Grade by Grade
E. The Wave Nature of Light · The Wave Nature of Light

Diffraction and Huygens' Principle

E2.1 E2.2 E3.1 E3.2About 65 minutes
Learning goals
  • I can describe diffraction of water waves through openings and around obstacles.
  • I can predict how the amount of diffraction depends on the ratio λ/w.
  • I can state Huygens' principle and use it to construct new wavefronts and explain straight-line travel, refraction and diffraction.
  • I can explain why we hear around corners but cannot see around them.

Words to know

diffraction
The bending and spreading of a wave as it passes through an opening or around the edge of an obstacle.
aperture
An opening, such as a gap in a barrier or a slit, that a wave passes through. Its width is written w.
Huygens' principle
Every point on a wavefront can be treated as a point source of tiny secondary wavelets that travel outward at the wave speed; the new wavefront is the line tangent to all the wavelets.
wavelet
A small circular wave imagined to start at one point on a wavefront in Huygens' principle.
envelope
The line (or surface) that just touches every wavelet at the same moment; it is the new wavefront.
rectilinear propagation
Travel in straight lines, as light seems to do in everyday life.

Around the corner

Your friend calls you from the kitchen. You are in the hallway and cannot see them, but you hear them perfectly. Sound reaches you around the door frame, while light does not seem to. Why would two waves behave so differently?

The answer is diffraction, and it depends on one simple ratio: the wavelength compared with the size of the opening. Diffraction is also the key that unlocks the rest of this unit, from Young's experiment to the resolution limit of a telescope.

Diffraction in a ripple tank

Send straight waves toward a barrier with a gap of width w. On the far side:

  • If the gap is wide compared with λ, the waves go through almost unchanged. Only the edges of the wavefronts curve a little, and a sharp "shadow" is left behind the barrier.
  • If the gap is about the same size as λ (or smaller), the waves spread out in almost perfect semicircles, filling the region behind the barrier.

The amount of diffraction depends on λ/w:

  • Larger λ (lower frequency) → more diffraction.
  • Narrower opening → more diffraction.
  • Diffraction becomes obvious when λ/w is roughly 1 or larger, and is barely noticeable when λ is much smaller than w.

Waves also diffract around the edges of obstacles. Diffraction does not change the wave's speed, frequency or wavelength, because the wave stays in the same medium; only its direction spreads.

gap ≈ λ: strong spreadinggap ≫ λ: little spreading
Straight water waves (seen from above, crests drawn as lines) meet a barrier. Left: the gap is about one wavelength wide, so the waves spread out in semicircles. Right: the gap is much wider than λ, so the waves pass almost straight through and only the edges bend. The wavelength is the same on both sides of the barrier.

Huygens' principle

In 1690 the Dutch scientist Christiaan Huygens published a simple way to predict where a wavefront will be next:

Every point on a wavefront acts as a source of tiny circular wavelets that spread forward at the speed of the wave. A moment later, the new wavefront is the line that touches (is tangent to) all of the wavelets. This tangent line is called the envelope.

To use it, pick a few points on the wavefront, draw a circle of radius r = vt around each one, and join the front edges of the circles.

  • A straight wavefront produces a new straight wavefront, parallel to the old one: this is why light travels in straight lines in a uniform medium.
  • A circular wavefront produces a bigger circle centred on the same source.
  • At a boundary, wavelets in the slower medium have smaller radii, so the envelope tilts: this is refraction.
  • At a gap, only the points inside the gap make wavelets. The wavelets at the edges have no neighbours beside them to cancel their sideways spread, so the wave curves into the region behind the barrier: this is diffraction. A narrow gap holds only a few wavelets, so the wave leaving it looks like a single circular source.
old wavefrontnew wavefrontstraight wave: wavelets from every pointsourcecircular wave: the envelope is a bigger circle
Huygens' construction. Each dot on the old wavefront sends out a wavelet (dashed) of radius vt. The new wavefront (solid) is the envelope touching all the wavelets: straight for a straight wave (left), a larger circle for a circular wave (right).
Worked example

Example 1: Will it diffract much?

In a ripple tank, a straight-wave generator vibrates at 8.0 Hz, and the waves travel at 20 cm/s. The waves meet a gap that is (a) 2.0 cm wide, then (b) 10 cm wide. Compare the diffraction.

  1. Wavelength: λ = v/f = 20 ÷ 8.0 = 2.5 cm.
  2. (a) λ/w = 2.5 ÷ 2.0 = 1.25. The gap is about one wavelength, so the waves spread out strongly, almost in semicircles.
  3. (b) λ/w = 2.5 ÷ 10 = 0.25. The gap is four wavelengths wide, so there is only a little bending at the edges.

The 2.0 cm gap gives much more diffraction. To get more diffraction through the wide gap, lower the frequency (longer λ).

Worked example

Example 2: Sound versus light at a doorway

A doorway is 0.90 m wide. Compare λ/w for (a) a 512 Hz note from a piano (speed of sound 343 m/s) and (b) green light of wavelength 550 nm.

  1. (a) λ = 343 ÷ 512 = 0.670 m, so λ/w = 0.670 ÷ 0.90 = 0.74.
  2. (b) λ/w = 550 × 10⁻⁹ ÷ 0.90 = 6.1 × 10⁻⁷.
  3. Sound has λ/w close to 1, so it diffracts strongly around the door frame. Light has λ/w less than one millionth, so its diffraction is far too small to notice.

You hear around the corner because the sound's wavelength is similar to the doorway's width; light's wavelength is about a million times too small.

Worked example

Example 3: A Huygens construction with numbers

A straight wavefront travels at 12 cm/s. Using Huygens' principle, how far ahead of the old wavefront is the new wavefront after 0.25 s, and what radius should you draw for each wavelet?

  1. Each wavelet travels at the wave speed: r = vt = 12 × 0.25 = 3.0 cm.
  2. Draw circles (or semicircles facing forward) of radius 3.0 cm centred on several points of the old wavefront.
  3. The envelope is a straight line parallel to the old wavefront, 3.0 cm ahead.

Draw wavelets of radius 3.0 cm; the new wavefront is 3.0 cm ahead and parallel to the old one.

Diffraction in everyday life

  • Radio: AM radio stations broadcast at about 530 to 1700 kHz, so their wavelengths are roughly 180 to 570 m. Those long waves diffract around hills and large buildings. FM waves (88 to 108 MHz) are only about 3 m long, so hills cast stronger "radio shadows" and FM reception fades sooner behind them.
  • Harbours: ocean waves diffract through a harbour entrance and spread into the harbour. Engineers think about this when designing breakwaters.
  • Light: light does diffract, but you need an opening or object about as small as a few wavelengths (a fraction of a millimetre or less) to notice it. That is why it took until the early 1800s for scientists to be convinced light is a wave, as the lesson on the wave–particle debate will show.
Just for fun

A radio wave and a light wave both try to sneak around a corner to listen in on a conversation. Only one succeeds. The other gets told off for being too short-sighted: its wavelength was a million times too small.

Hands-on activity

A ripple tank in a baking dish

You need: a clear glass baking dish, water, a desk lamp or a phone flashlight, a sheet of white paper, a ruler, and two small heavy blocks (for example, two wooden blocks or two bricks of building toy pieces).

Grown-up note: keep the lamp, its cord and any plugs well away from the water, and wipe up spills.

  1. Put the dish on the white paper on a table and fill it with about 1 cm of water. Shine the light from above, so the shadows of the ripples show on the paper.
  2. Lay the ruler in the water at one end and tap it gently and steadily to make straight waves.
  3. Place the two blocks across the middle of the dish with a gap between them. Start with a gap of about 6 cm, then make it about 1 cm.
  4. Watch the waves beyond the gap. Then tap faster (shorter λ) and slower (longer λ) with the same gap.
  5. Finally, put one block alone in the middle and watch waves bend around its edges.

What to look for: with the narrow gap, the waves spread out in curves behind the barrier; with the wide gap, they go mostly straight through. Tapping slower (longer λ) increases the spreading. Sketch each case and label λ and w.

Your turn

1

Define diffraction.

2

State two ways to increase diffraction through a gap.

3

Does diffraction change a wave's wavelength? Explain.

4

Water waves with λ = 1.5 cm pass through a 1.5 cm gap and then a 9.0 cm gap. Which gives more diffraction?

5

State Huygens' principle in your own words.

6

Why can you hear a radio playing in another room but not see it?

7

A wave travels at 30 cm/s. What radius should Huygens wavelets have to find the wavefront 0.10 s later?

More practice: warm-up

1

Which diffracts more around a building: an AM radio wave or an FM radio wave?

2

What is an aperture?

3

In what year did Huygens publish his principle?

4

Fill in: diffraction is noticeable when the opening is about the same size as the ___.

5

Do waves diffract around the edges of obstacles as well as through gaps?

More practice: on your own

1

A ripple-tank wave generator runs at 5.0 Hz, and the waves travel at 15 cm/s. The waves pass through a 3.0 cm gap. Find λ/w and predict the amount of diffraction.

2

In the same tank, the frequency is raised to 15 Hz. What happens to the diffraction through the 3.0 cm gap? Explain.

3

Use Huygens' principle to explain why a wave refracts when it crosses at an angle into slower water.

4

Explain why a narrow gap acts almost like a single point source of circular waves.

5

Whales can communicate using sound with frequencies near 20 Hz. In seawater (v ≈ 1500 m/s), find λ and explain why these sounds pass around large undersea obstacles easily.

Challenge

1

A harbour entrance is 40 m wide. Ocean swell has a period of 8.0 s and travels at 12 m/s. Will the waves spread strongly into the harbour? What would engineers prefer, and why?

2

The opening of a loudspeaker is 0.30 m across. Find the frequencies for which λ equals the speaker width, and explain why high notes from a speaker are heard best when you stand right in front of it (use v = 343 m/s).

3

A doorway is 0.80 m wide. What wavelength of light would diffract as strongly through it as a 400 Hz sound (v = 343 m/s)? Is that light visible?

Check your understanding

Quiz

1.

Which change increases the diffraction of water waves through a gap?

2.

When a wave diffracts through a gap, its wavelength…

3.

In Huygens' principle, the new wavefront is…

4.

Why is diffraction of light hard to notice in everyday life?

5.

A ripple tank has waves with λ = 2.0 cm. Which gap gives the greatest diffraction?

6.

Which explains why AM radio reception is often better than FM behind hills?

For parents and teachers

Big idea: diffraction depends on λ/w. Students should leave this lesson able to predict, with reasons, whether diffraction will be noticeable (expectations E3.1 and E3.2, investigated through E2.2).

How to help: the baking-dish ripple tank works best with shallow water and a bright light directly above. If it is hard to see, a free ripple-tank simulation (for example, PhET Wave Interference, with a barrier and slit) shows the same thing very clearly.

Common difficulties:

  • Thinking the wavelength changes after a gap. It does not.
  • Mixing up the direction of the relationship: narrower gap and longer wavelength mean more diffraction.
  • Treating Huygens wavelets as real separate waves. They are a construction tool: a way to predict where the wavefront goes next.