3. Diffraction

Diffraction

Diffraction is the spreading or bending of waves when they pass through an opening or travel around the edge of an obstacle.

Diffraction is a fundamental property of waves and can occur with:

• water waves
• sound waves
• light waves
• radio waves
• microwaves
• seismic waves

The amount of diffraction depends strongly on the relationship between the wavelength and the size of the opening or obstacle.

---

What Is Diffraction?

When a wave encounters an opening or obstacle, it does not always continue only in a straight line.

Instead, the wave can spread into regions that would otherwise appear to be behind the barrier.

This spreading is called:

diffraction

For example, water waves passing through a narrow gap can spread outward in curved wavefronts.

Similarly, sound can travel around a doorway or corner even when the sound source cannot be seen directly.

---

Diffraction Through an Opening

Imagine straight water-wave fronts approaching a gap in a barrier.

After passing through the gap, the waves spread outward.

The amount of spreading depends on:

• wavelength, λ
• width of the opening

If the opening is very wide compared with the wavelength, there is relatively little spreading.

If the opening is similar in size to the wavelength, there is strong spreading.

---

When Is Diffraction Greatest?

Diffraction is especially noticeable when the size of the opening is approximately comparable to the wavelength.

A useful rule is:

opening size ≈ wavelength → strong diffraction

If the opening becomes smaller relative to the wavelength, spreading can become even more pronounced, although less wave energy may pass through a very small opening.

If:

opening size ≫ wavelength

the waves mainly continue forward with only limited spreading near the edges.

---

Comparing Gap Sizes

Suppose waves have wavelength:

λ = 2 m

Consider three openings.

Opening A = 20 m

The opening is much larger than the wavelength.

Result:

little diffraction

Opening B = 2 m

The opening is approximately equal to the wavelength.

Result:

strong diffraction

Opening C = 1 m

The opening is smaller than the wavelength.

Result:

very strong spreading of the transmitted wave, although the amount of transmitted energy may be reduced.

---

Wide Opening

When the opening is much wider than the wavelength:

gap ≫ λ

most of the wavefront continues approximately straight.

Diffraction occurs mainly near the edges.

The central part of the wavefront remains relatively straight.

This is sometimes described as:

weak diffraction

---

Opening Similar to the Wavelength

When:

gap ≈ λ

the wave spreads strongly after passing through the opening.

The outgoing wavefront can become approximately semicircular in a two-dimensional ripple-tank model.

This is one of the clearest demonstrations of diffraction.

---

Very Narrow Opening

When an opening is narrow compared with the wavelength, the portion of the wave that passes through can spread through a very large range of directions.

The opening behaves approximately like a new source of waves.

This idea helps explain why narrow gaps can produce strongly curved outgoing wavefronts.

---

Wavelength and Diffraction

For a fixed opening:

longer wavelength → more noticeable diffraction

shorter wavelength → less noticeable diffraction

The wavelength must always be considered relative to the dimensions of the obstacle or opening.

It is therefore better to ask:

How large is the wavelength compared with the gap or obstacle?

rather than simply asking whether the wavelength is "long" or "short."

---

Comparing Two Wavelengths

Suppose an opening is:

1 m wide

Wave A has:

λ = 0.10 m

Wave B has:

λ = 1.0 m

For Wave A:

gap = 10λ

The opening is much wider than the wavelength.

Diffraction is relatively small.

For Wave B:

gap = λ

The opening is comparable to the wavelength.

Diffraction is strong.

Therefore:

Wave B diffracts more strongly.

---

Diffraction Around an Obstacle

Waves can also diffract around the edges of obstacles.

Instead of creating a perfectly sharp wave-free region behind the obstacle, waves can bend into the region behind it.

The amount of diffraction depends on the obstacle's size relative to the wavelength.

---

Large Obstacles

Suppose the obstacle is much larger than the wavelength.

Then:

obstacle size ≫ wavelength

diffraction around the edges is relatively limited.

A substantial wave shadow can form behind the obstacle.

This is one reason short-wavelength waves tend to produce sharper shadow regions.

---

Obstacles Comparable to the Wavelength

If the obstacle is similar in size to the wavelength, diffraction becomes much more noticeable.

The waves bend around the edges and can enter the region behind the obstacle.

Therefore:

obstacle size ≈ wavelength → significant diffraction

---

Diffraction Does Not Mean the Wave Changes Speed

Diffraction is different from refraction.

During diffraction in the same medium:

• wave speed remains the same
• frequency remains the same
• wavelength remains the same

What changes is mainly:

the direction in which the wave energy spreads

This is an important distinction.

---

Diffraction vs Refraction

Diffraction

occurs when waves spread around obstacles or through openings.

Refraction

occurs when wave speed changes as a wave enters a different region or medium.

During diffraction in the same medium:

v, f, and λ remain unchanged

During refraction:

v and λ can change while f remains constant

---

Diffraction vs Reflection

Reflection

causes a wave to return from a boundary.

Diffraction

causes a wave to spread around an edge or through an opening.

For example, when water waves encounter a harbour wall:

• some waves may reflect from the wall
• waves passing the end of the wall may diffract around it

Several wave behaviours can therefore occur in the same situation.

---

Comparing Reflection, Refraction, and Diffraction

All three are general wave behaviours.

---

Water-Wave Diffraction

Water waves provide an easy way to observe diffraction.

In a ripple tank, straight wavefronts can be directed toward a barrier containing a gap.

When the gap is wide compared with the wavelength:

• most wavefronts continue straight
• some spreading occurs near the edges

When the gap is comparable to the wavelength:

• the wave spreads strongly
• curved wavefronts emerge

---

Changing the Gap Width

Suppose wavelength stays constant.

If the gap becomes progressively narrower:

diffraction generally becomes more noticeable

when the gap becomes comparable to the wavelength.

This is why ripple-tank experiments often use an adjustable gap.

Students can change the opening while keeping the wave source approximately constant.

---

Changing the Wavelength

Suppose gap width stays constant.

Increasing the wavelength makes the gap smaller relative to the wavelength.

Therefore:

longer wavelength → stronger diffraction

Decreasing wavelength makes the gap larger relative to the wavelength.

Therefore:

shorter wavelength → weaker diffraction

---

Sound Diffraction

Sound waves have wavelengths large enough that diffraction is common in everyday life.

This is why you can often hear someone:

• around a corner
• through an open doorway
• behind an obstacle
• on the other side of a partially open barrier

The sound waves diffract around edges and through openings.

---

Hearing Around a Corner

Suppose someone is speaking in a hallway around a corner.

There is no straight line between the speaker and listener.

However, sound waves can diffract around the corner.

Some sound energy reaches the listener.

Therefore:

you can hear someone you cannot see.

This is a simple everyday example of diffraction.

---

Low- and High-Frequency Sound

For sound travelling at approximately the same speed:

v = fλ

Therefore:

λ = v/f

Lower-frequency sound has a:

longer wavelength

Higher-frequency sound has a:

shorter wavelength

Since longer wavelengths generally diffract more strongly around a given obstacle:

low-frequency sounds tend to bend around large obstacles more effectively than high-frequency sounds.

---

Worked Example: Sound Wavelength

Assume the speed of sound is:

340 m/s

A low-frequency sound has:

f = 170 Hz

Calculate wavelength:

λ = v/f

λ = 340/170

λ = 2.0 m

Now consider a sound with:

f = 3400 Hz

λ = 340/3400

λ = 0.10 m

The 170 Hz sound has a much longer wavelength.

It will generally show more noticeable diffraction around metre-scale obstacles.

---

Why Bass Can Be Heard Around Obstacles

Bass sounds have relatively low frequencies and long wavelengths.

Their wavelengths may be comparable to the sizes of:

• doorways
• walls
• vehicles
• buildings

As a result, low-frequency sound can diffract significantly.

This is one reason bass from music may remain noticeable even when the source is behind an obstacle.

---

Light Diffraction

Light is also a wave and therefore undergoes diffraction.

However, visible-light wavelengths are extremely small:

approximately:

380–750 nm

or:

3.8 × 10⁻⁷ m to 7.5 × 10⁻⁷ m

Everyday objects and openings are usually enormously larger than these wavelengths.

Therefore, diffraction of visible light is often difficult to notice in ordinary situations.

---

Why Light Appears to Travel in Straight Lines

A doorway might be approximately:

1 m wide

Visible-light wavelength is approximately:

10⁻⁷ m

The doorway is therefore millions of wavelengths wide.

Consequently, diffraction is extremely small on the everyday scale.

Light therefore appears to travel in nearly straight lines and can produce sharp shadows.

Sound, with much longer wavelengths, can spread around the same doorway much more noticeably.

---

Diffraction of Light Through a Narrow Slit

If light passes through an extremely narrow slit whose dimensions become sufficiently small relative to its wavelength, diffraction becomes observable.

Instead of producing a perfectly sharp narrow line on a screen, the light spreads into a pattern.

A typical single-slit diffraction pattern includes:

• a broad central bright region
• darker regions
• weaker bright regions on either side

This provides strong evidence that light behaves as a wave.

---

Diffraction and Wave Evidence

Diffraction is characteristic of wave behaviour.

Experiments showing light diffraction helped establish that light has wave properties.

Today, light is understood through quantum physics, but diffraction remains one of the clearest demonstrations of its wave behaviour.

---

Radio-Wave Diffraction

Radio waves can have wavelengths much longer than visible light.

Depending on their frequency, some radio waves can diffract around:

• buildings
• hills
• other large obstacles

This can allow signals to reach regions without a perfectly clear line of sight.

The amount of diffraction depends on the wavelength and the dimensions of the obstacle.

---

Radio Frequency and Wavelength

Since:

v = fλ

and electromagnetic waves in air travel at approximately the same speed:

lower-frequency radio waves generally have:

longer wavelengths

Higher-frequency electromagnetic waves generally have:

shorter wavelengths

Longer-wavelength signals can therefore show stronger diffraction around a given obstacle.

---

Communication Systems

Diffraction is important when engineers design communication systems.

They must consider:

• transmitter frequency
• wavelength
• buildings
• terrain
• antenna positions
• line of sight

Different frequencies behave differently around obstacles.

This affects technologies such as:

• radio broadcasting
• wireless communication
• navigation systems
• telecommunications

---

Microwaves and Diffraction

Microwaves also undergo diffraction.

Their wavelengths can range from approximately millimetres to tens of centimetres, depending on frequency.

Engineers must consider diffraction when designing:

• microwave communication links
• radar systems
• satellite communication
• antennas

At many microwave frequencies, obstacles such as buildings are much larger than the wavelength, so line-of-sight effects can become particularly important.

---

Diffraction Around Harbour Openings

Harbours provide a useful large-scale example of diffraction.

Ocean waves enter through an opening between harbour walls.

After passing through the entrance, the waves can spread into the sheltered region.

If the entrance width is comparable to the wavelength, significant diffraction can occur.

---

Breakwaters

A breakwater is a structure designed to reduce wave energy reaching a protected area.

However, waves can diffract around the ends of a breakwater.

Engineers must therefore consider:

• wavelength
• breakwater length
• harbour entrance width
• direction of incoming waves

A region behind a barrier may not be completely protected because waves can spread into it through diffraction.

---

Seismic-Wave Diffraction

Seismic waves can also diffract around structures and boundaries inside Earth.

Their wavelengths can be very large.

This means they can bend and spread around geological features.

Seismologists consider diffraction along with:

• reflection
• refraction
• wave-speed changes

when interpreting seismic data.

---

Diffraction and Shadows

Diffraction explains why wave shadows are not always perfectly sharp.

For short wavelengths relative to an obstacle:

sharper shadow

For wavelengths comparable to the obstacle:

greater spreading into the shadow region

This explains why:

• visible light often produces relatively sharp shadows
• sound can reach behind obstacles

---

The Huygens Idea

A useful model for understanding diffraction is Huygens' principle.

It treats each point on a wavefront as a source of small secondary wavelets.

The next wavefront is formed from the combined effect of these wavelets.

At an opening or edge, some of these wavelets spread into regions that would otherwise be behind the barrier.

This helps explain why waves diffract.

---

Diffraction Through a Narrow Gap Using Huygens' Principle

Imagine a plane wave reaching a very narrow gap.

Only a small portion of the original wavefront passes through.

The opening then behaves approximately like a point source.

The outgoing waves spread in many directions.

In two dimensions, the resulting wavefronts can appear approximately semicircular.

This explains the strong diffraction seen in ripple-tank experiments.

---

Diffraction Around an Edge

Huygens' principle also helps explain diffraction around an obstacle.

Points on the wavefront near the edge act as sources of secondary wavelets.

These wavelets spread into the region behind the obstacle.

Therefore, the boundary of the wave shadow is not perfectly sharp.

---

Predicting Diffraction from a Diagram

When given a wave diagram, compare:

λ = wavelength

with:

a = opening or obstacle size

If:

a ≫ λ

predict:

little diffraction

If:

a ≈ λ

predict:

strong diffraction

If:

a < λ

predict:

very strong angular spreading of the transmitted wave, although transmission through a very small opening may be reduced.

---

Example: Comparing Three Waves

A gap is:

2 m wide

Wave A:

λ = 0.1 m

Wave B:

λ = 1.5 m

Wave C:

λ = 2.0 m

Compare the ratios.

Wave A:

2/0.1 = 20 wavelengths across

Diffraction is relatively weak.

Wave B:

2/1.5 ≈ 1.3 wavelengths across

Diffraction is strong.

Wave C:

2/2 = 1 wavelength across

Diffraction is very strong.

Therefore, Wave C produces the greatest spreading of the three.

---

Example: Changing Frequency

Two sound waves travel through the same air.

Wave A:

f = 200 Hz

Wave B:

f = 2000 Hz

Because they travel at approximately the same speed:

Wave A has the longer wavelength.

Therefore, around the same obstacle:

Wave A generally diffracts more strongly.

This shows the connection:

lower frequency → longer wavelength → greater diffraction

when wave speed and obstacle size remain approximately constant.

---

Diffraction Does Not Create New Waves

When a wave diffracts, it may look as though new waves are being produced at an opening.

However, the outgoing wave is the continuation of the original disturbance.

Its energy has been redistributed across a wider range of directions.

Diffraction changes the spatial distribution of wave energy.

It does not create energy.

---

Energy and Diffraction

As a wave spreads over a larger region, its energy is distributed over that region.

Therefore, strong spreading does not mean that every point receives the same intensity as the original wave.

The shape and intensity of a real diffraction pattern depend on factors such as:

• wavelength
• opening geometry
• distance from the opening
• original wave amplitude

---

Applications of Diffraction

Diffraction has many practical consequences.

Sound

Allows sound to spread around obstacles and through openings.

Radio communication

Helps some radio signals reach behind hills and buildings.

Harbours

Causes water waves to spread through harbour entrances and around breakwaters.

Optical instruments

Diffraction places a fundamental limit on resolution.

Spectroscopy

Diffraction gratings can separate light according to wavelength.

Astronomy

Diffraction affects the smallest details telescopes can resolve.

Microscopy

Diffraction limits how closely spaced structures can be distinguished using ordinary light.

---

Diffraction Gratings

A diffraction grating contains many closely spaced parallel lines or openings.

Light passing through or reflecting from the grating diffracts.

The diffracted waves interfere with one another.

Different wavelengths emerge strongly at different angles.

This allows a diffraction grating to separate light into a spectrum.

Diffraction gratings are widely used in:

• spectrometers
• laboratory instruments
• astronomy
• chemical analysis

---

Diffraction and Optical Resolution

Even a perfect optical instrument cannot resolve infinitely small details.

Light passing through a finite aperture diffracts.

This produces a small diffraction pattern rather than an infinitely sharp point.

Therefore, diffraction places a fundamental limit on the resolution of:

• telescopes
• microscopes
• cameras

Larger apertures generally reduce diffraction spreading and improve potential resolution for a given wavelength.

---

A Complete Water-Wave Example

Water waves have:

λ = 4 cm

They approach a barrier with a:

20 cm opening.

The opening is:

20/4 = 5 wavelengths wide.

Some diffraction occurs, especially near the edges, but the wavefront remains substantially forward-directed.

The opening is then reduced to:

4 cm.

Now:

gap = wavelength.

Strong diffraction occurs.

The waves spread broadly beyond the opening.

The wavelength has not changed because the waves remain in the same water conditions.

Only their pattern of propagation has changed.

---

A Complete Sound Example

A sound wave travels through air at:

340 m/s

with frequency:

170 Hz

Its wavelength is:

λ = v/f

λ = 340/170

λ = 2.0 m

The sound reaches a doorway approximately:

2 m wide.

Therefore:

doorway width ≈ wavelength

Significant diffraction can occur.

The sound can spread through the doorway into a wide range of directions.

This helps explain why a person inside the room can hear the sound even without standing directly in front of the doorway.

---

A Reliable Strategy for Diffraction Problems

When analyzing diffraction:

1. Identify the type of wave.
2. Determine the wavelength if it is given.
3. If necessary, calculate wavelength using λ = v/f.
4. Identify the width of the opening or size of the obstacle.
5. Compare this size with the wavelength.
6. If the opening is much larger than λ, predict limited diffraction.
7. If the opening is comparable to λ, predict strong diffraction.
8. If the opening is smaller than λ, predict very strong angular spreading of the transmitted wave.
9. For obstacles, consider how much the wave can spread into the shadow region.
10. Remember that frequency does not change simply because diffraction occurs.
11. Remember that speed and wavelength also remain unchanged if the wave remains in the same medium.
12. Sketch the outgoing wavefronts with appropriate curvature.

---

Common Mistakes

Thinking diffraction is refraction

Diffraction involves spreading around edges or through openings.

Refraction involves a change in wave speed.

Thinking diffraction requires a new medium

A wave can diffract while remaining entirely in the same medium.

Thinking wavelength changes during diffraction

If the medium remains unchanged, speed and frequency remain unchanged, so wavelength remains unchanged.

Thinking only water waves diffract

All waves can diffract.

Thinking light does not diffract

Light does diffract, but its very short wavelength makes everyday diffraction difficult to notice.

Thinking sound travels around corners because it reflects from everything

Reflection may contribute in real environments, but diffraction itself allows sound to spread around edges.

Thinking diffraction occurs only through gaps

Waves also diffract around obstacles and edges.

Thinking a narrow opening always produces more transmitted energy

A narrower opening can produce greater angular spreading while allowing less total wave energy through.

Thinking longer wavelengths always diffract more in every situation

The important factor is the wavelength relative to the size of the opening or obstacle.

Thinking a diffracted wave has gained energy

Diffraction redistributes existing wave energy; it does not create energy.

---

Key Terms

Diffraction — spreading of waves as they pass through openings or around obstacles.

Wavelength (λ) — distance between corresponding points on consecutive wave cycles.

Opening — gap through which a wave can pass.

Obstacle — object that blocks part of an incoming wave.

Wavefront — line joining points on a wave that are at the same stage of oscillation.

Wave shadow — region behind an obstacle receiving reduced wave energy.

Ripple tank — apparatus used to observe water-wave behaviour.

Huygens' principle — model in which points on a wavefront act as sources of secondary wavelets.

Secondary wavelet — small wave used in Huygens' model to construct the next wavefront.

Single-slit diffraction — spreading of a wave after passing through one narrow opening.

Diffraction grating — structure containing many closely spaced lines or openings that produces diffraction and interference.

Resolution — ability of an instrument to distinguish closely spaced details.

Aperture — opening through which a wave enters an optical or other wave system.

Shadow region — region behind an obstacle where direct wave propagation is blocked.

Frequency (f) — number of complete wave cycles passing a point each second.

Wave speed (v) — rate at which a wave disturbance propagates.

---

Key Takeaways

• Diffraction is the spreading of waves through openings and around obstacles.
• All types of waves can undergo diffraction.
• The amount of diffraction depends strongly on wavelength relative to opening or obstacle size.
• Diffraction is especially noticeable when the opening is comparable to the wavelength.
• A wave can spread very strongly when an opening is smaller than its wavelength, although less energy may be transmitted.
• A wide opening compared with wavelength produces relatively little diffraction.
• Longer wavelengths generally diffract more strongly around a fixed-size opening or obstacle.
• Shorter wavelengths generally produce less diffraction for the same geometry.
• During diffraction in the same medium, speed remains unchanged.
• Frequency remains unchanged.
• Wavelength remains unchanged.
• Diffraction changes the directions over which wave energy propagates.
• Waves can diffract around obstacles into regions that would otherwise be wave shadows.
• Sound diffraction explains why sounds can often be heard around corners.
• Low-frequency sound generally has longer wavelengths and diffracts more noticeably around everyday obstacles.
• Visible light diffracts, but its wavelength is extremely short compared with most everyday objects.
• Narrow slits can produce observable diffraction patterns with light.
• Water-wave diffraction can be clearly observed in a ripple tank.
• Radio waves can diffract around large obstacles depending on their wavelengths.
• Ocean waves can diffract through harbour openings and around breakwaters.
• Diffraction gratings use diffraction and interference to separate wavelengths.
• Diffraction places a fundamental limit on the resolution of optical instruments.
• Huygens' principle provides a useful model for explaining how waves spread around edges and through openings.
• Reflection, refraction, and diffraction are distinct but fundamental wave behaviours.

---

Check Your Understanding

1. Define diffraction.
2. Describe what happens when straight water waves pass through a narrow opening.
3. Under what condition is diffraction especially noticeable?
4. Waves with a wavelength of 3 cm approach two openings. Opening A is 30 cm wide and Opening B is 3 cm wide. Predict which opening will produce greater diffraction and explain why.
5. Explain how the amount of diffraction changes when wavelength increases while gap width remains constant.
6. Explain how the amount of diffraction changes when gap width decreases while wavelength remains constant.
7. Describe how waves can diffract around an obstacle and explain what happens in the wave-shadow region.
8. A sound wave travels at 340 m/s and has a frequency of 170 Hz. Calculate its wavelength. Would you expect significant diffraction through a doorway approximately 2 m wide? Explain.
9. Two sounds have frequencies of 200 Hz and 2000 Hz and travel through the same air. Which one is likely to diffract more strongly around a large obstacle? Explain using wavelength.
10. Explain why sound can often be heard around a corner even when the sound source cannot be seen.
11. Visible light and sound both pass through a doorway. Explain why sound generally shows much more obvious diffraction than visible light.
12. During diffraction, what happens to the wave's speed, frequency, and wavelength if the medium does not change?
13. Compare diffraction, reflection, and refraction. Describe the main cause and behaviour associated with each.
14. Explain why diffraction is important when engineers design harbour entrances, breakwaters, communication systems, microscopes, or telescopes.
15. A student says, "If I make a gap narrower, the wavelength of the wave becomes shorter and that causes more diffraction." Explain what is wrong with this statement and give the correct relationship between gap size, wavelength, and diffraction.