Interference and Diffraction

Overview

Interference and diffraction are important wave behaviours explained by the principle of superposition.

• Interference occurs when waves overlap and combine.
• Diffraction is the spreading of waves through gaps or around obstacles.

These ideas are central to optics, sound, microwaves, and later topics in modern physics.

Definition

Interference is the formation of a resultant pattern when two or more coherent waves overlap.

Diffraction is the spreading of waves when passing through a gap or around an obstacle.

Why It Matters

These phenomena provide strong evidence of wave behaviour. They also connect qualitative reasoning with standard exam formulas for fringes, path difference, gratings, and wave spreading.

Key Representations

Principle of Superposition

When two or more waves meet, the resultant displacement at any point is the algebraic sum of the individual displacements.

If:

• displacements are in same direction → reinforce
• displacements are in opposite directions → cancel partly or fully

This principle underlies interference and stationary waves.

What Is Interference?

The interference pattern may contain:

• maxima (constructive interference)
• minima (destructive interference)

Coherent Sources

Stable interference requires sources that are:

• same frequency
• constant phase difference
• same type of wave
• similar amplitude (best visibility)

Example:

• double slit illuminated by one source

Constructive Interference

Waves arrive in phase.

Path difference:

$$n\lambda$$

where:

$$n=0,1,2,3,\dots$$

Result:

• maximum amplitude
• maximum intensity

Destructive Interference

Waves arrive in antiphase.

Path difference:

$$\left(n+\frac{1}{2}\right)\lambda$$

Result:

• minimum amplitude
• zero intensity (ideal equal amplitudes)

Young Double-Slit Idea

Two coherent slits produce bright and dark fringes on a screen.

Central Bright Fringe

Occurs when path difference is zero.

Fringe Spacing

For slit separation $a$, screen distance $D$:

$$w=\frac{\lambda D}{a}$$

where $w$ is fringe spacing.

Worked Example: Fringe Spacing

Given:

• $\lambda =6.0\times 10^{-7}\text{ m}$
• $D=2.0\text{ m}$
• $a=4.0\times 10^{-4}\text{ m}$

$$w=\frac{\lambda D}{a}=\frac{(6.0\times 10^{-7})(2.0)}{4.0\times 10^{-4}}$$ $$w=3.0\times 10^{-3}\text{ m}=3.0\text{ mm}$$

What Is Diffraction?

Diffraction is the spreading of waves when passing through a gap or around an obstacle.

Occurs for all wave types.

Examples:

• sound heard around corners
• water waves through harbour opening
• light through narrow slit

When Is Diffraction Most Significant?

Diffraction is strongest when:

$$\text{gap size}\sim \lambda$$

If gap is much larger than wavelength:

• little spreading

If gap is comparable to wavelength:

• strong spreading

Single-Slit Trends

As slit width decreases:

• diffraction increases
• central maximum becomes wider

As wavelength increases:

• diffraction increases

Why Sound Diffracts More Easily Than Light

Typical sound wavelength is much larger than visible-light wavelength.

So everyday openings are often comparable to sound wavelengths but enormous compared with light wavelengths.

Hence:

• sound bends around doors
• light mostly travels straight

Diffraction Grating

A diffraction grating has many equally spaced slits.

Produces sharp maxima satisfying:

$$d\sin \theta =n\lambda$$

where:

• $d$ = slit spacing
• $\theta$ = angle of maximum
• $n=0,1,2,\dots$

Used to measure wavelength and separate spectra.

Worked Example: Grating

Given:

• $d=2.0\times 10^{-6}\text{ m}$
• first-order maximum at $30^{\circ }$

$$d\sin \theta =\lambda$$ $$\lambda =(2.0\times 10^{-6})\sin 30^{\circ }$$ $$\lambda =1.0\times 10^{-6}\text{ m}$$

Interference vs Diffraction

Feature	Interference	Diffraction
Cause	Overlap of waves from sources/paths	Spreading through gap/edge
Pattern	Repeated maxima/minima	Central maximum + side maxima
Needs coherence	Usually yes	No separate coherent sources needed
Example	Double slit fringes	Single slit spreading

Link to Stationary Waves

Stationary waves are also produced by superposition, but involve two opposite-travelling waves of same frequency.

See Stationary Waves.

Common Exam Pitfalls

• using path difference instead of phase difference carelessly
• forgetting coherence requirement
• saying destructive interference means waves disappear permanently
• confusing diffraction with refraction
• thinking only light diffracts
• using grating equation with wrong order $n$

Quick Revision Checklist

Ask:

• Is this interference or diffraction?
• Are the sources coherent?
• Constructive or destructive condition?
• Is gap size comparable to wavelength?
• Should I use fringe spacing or grating formula?

Formula Summary

$$\text{Constructive: }n\lambda$$ $$\text{Destructive: }\left(n+\frac{1}{2}\right)\lambda$$ $$w=\frac{\lambda D}{a}$$ $$d\sin \theta =n\lambda$$

Related Links

• Waves
• Stationary Waves
• Superposition of Waves
• Quantum Physics

Links

• Main topic: Waves
• Related concept: Stationary Waves
• Related topic: Superposition of Waves
• Related topic: Quantum Physics

Summary

Interference is wave combination producing maxima and minima. Diffraction is wave spreading through gaps or around obstacles. Both are strong evidence of wave behaviour and follow from superposition.