Diffraction Examples

Why This Matters

Diffraction sits at the heart of wave physics and shows up repeatedly on the College Physics exam—not as isolated trivia, but as proof that you understand wave behavior. When waves encounter obstacles or apertures, they don't just stop or pass through unchanged; they bend, spread, and interfere. You're being tested on whether you can predict patterns, apply key equations like the single-slit minimum condition or Bragg's law, and explain why wavelength-to-aperture ratios matter.

The examples below demonstrate core principles: interference and superposition, resolution limits, wavelength dependence, and the universal nature of wave phenomena across light, sound, and water. Don't just memorize what each setup looks like—know why the pattern forms and how changing variables affects the result. That's what earns you points on FRQs.

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Slit-Based Diffraction: Apertures and Interference

When light passes through one or more narrow openings, it spreads out and creates characteristic intensity patterns. The key physics here is path difference—waves from different parts of the aperture travel different distances and interfere constructively or destructively.

Single Slit Diffraction

• Central maximum dominates—the bright central band is twice as wide as the secondary maxima, with intensity falling off rapidly for higher-order fringes
• Narrower slits produce wider patterns—this inverse relationship ($a \sin\theta = m\lambda$ for minima) is a classic exam question; smaller aperture means more spreading
• Dark fringes occur at specific angles—minima appear where $\sin\theta = m\lambda/a$, with $m = \pm 1, \pm 2, ...$ (never zero)

Double Slit Diffraction

• Interference fringes appear within the diffraction envelope—the single-slit pattern from each slit modulates the two-source interference pattern
• Fringe spacing depends on slit separation—use $d \sin\theta = m\lambda$ for bright fringes; larger $d$ means closer spacing on the screen
• Demonstrates superposition principle—waves from both slits combine, proving light's wave nature (historically, Young's experiment)

Diffraction Gratings

• Many slits produce sharp, intense maxima—hundreds or thousands of slits create narrow peaks at angles given by $d \sin\theta = m\lambda$
• Used for spectral analysis—different wavelengths diffract at different angles, separating white light into its component colors
• Higher orders spread farther apart—the $m = 2$ maximum appears at a larger angle than $m = 1$, useful for resolving closely spaced wavelengths

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Aperture Shape and Resolution Limits

The geometry of an opening determines the diffraction pattern's shape. Circular apertures are especially important because they govern how well optical instruments can distinguish fine details.

Circular Aperture Diffraction (Airy Disk)

• Central bright spot surrounded by rings—the Airy disk pattern has a dominant central maximum with concentric rings of rapidly decreasing intensity
• Smaller apertures create larger disks—the angular radius of the first dark ring is $\theta \approx 1.22\lambda/D$, where $D$ is the aperture diameter
• Sets the resolution limit—two point sources are just resolvable when one's central maximum falls on the other's first minimum (Rayleigh criterion)

Diffraction in Optical Instruments (Telescopes, Microscopes)

• Diffraction limits resolution, not just lens quality—even a perfect lens can't focus light to a point smaller than the Airy disk
• Larger apertures improve resolution—this is why telescope mirrors are built as large as possible; doubling $D$ halves the minimum resolvable angle
• Shorter wavelengths also help—electron microscopes achieve higher resolution than optical ones because electron wavelengths are much smaller than visible light

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Diffraction in Other Wave Systems

Diffraction isn't unique to light—it's a universal wave phenomenon. Sound waves and water waves follow the same principles, with wavelength-to-obstacle ratios determining how much bending occurs.

Diffraction of Water Waves

• Waves spread after passing through gaps—when a water wave encounters a harbor entrance, it fans out into the protected area
• Wavelength comparable to opening size maximizes spreading—if the gap is much larger than $\lambda$, waves pass through with minimal diffraction
• Demonstrates wave behavior visually—ripple tanks make diffraction easy to observe, reinforcing concepts that apply to all wave types

Sound Wave Diffraction Around Obstacles

• Sound bends around corners—you can hear someone speaking around a wall because sound wavelengths (centimeters to meters) are comparable to everyday obstacle sizes
• Low frequencies diffract more than high frequencies—bass sounds spread around obstacles better because their longer wavelengths experience more bending
• Explains acoustic phenomena—this is why you hear the bass from a concert before the treble as you approach from outside

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Specialized Diffraction Applications

Some diffraction setups have specific applications in measurement and structural analysis. These examples show how diffraction becomes a tool, not just a phenomenon to observe.

Diffraction of Light by a Hair or Thin Wire

• Thin obstacles create measurable patterns—light bending around a hair produces alternating bright and dark fringes on a screen
• Can measure hair diameter—by analyzing fringe spacing and knowing the wavelength, you can calculate the obstacle's width (Babinet's principle)
• Confirms wave nature of light—the pattern matches predictions from wave theory, not particle models

X-ray Diffraction in Crystals

• Reveals atomic structure—X-rays have wavelengths comparable to atomic spacings, so crystal lattices act as natural diffraction gratings
• Bragg's law governs the pattern—constructive interference occurs when $2d \sin\theta = n\lambda$, where $d$ is the spacing between crystal planes
• Foundation of structural biology—this technique determined the structure of DNA and countless proteins (Nobel Prize-winning applications)

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Theoretical Framework: Near-Field vs. Far-Field

The mathematical treatment of diffraction depends on the distances involved. Understanding these regimes helps you know which equations apply.

Fresnel and Fraunhofer Diffraction

• Fraunhofer (far-field) assumes parallel rays—when source and screen are effectively at infinity, the math simplifies to the standard formulas you'll use on exams
• Fresnel (near-field) involves curved wavefronts—finite distances create more complex patterns requiring integration over the aperture
• Most exam problems use Fraunhofer conditions—if the problem gives you a distant screen or uses a lens to focus the pattern, assume far-field approximations apply

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Quick Reference Table

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Self-Check Questions

1. Which two examples best demonstrate how aperture size inversely affects pattern width, and what equation connects them?

2. A sound wave and a light wave both encounter an obstacle the size of a doorway. Which diffracts more noticeably, and why does wavelength matter?

3. Compare the intensity patterns from a single slit, double slit, and diffraction grating. How does increasing the number of slits change the sharpness of the maxima?

4. An FRQ asks you to explain why larger telescope mirrors produce sharper images. Which diffraction concept applies, and what equation would you cite?

5. Both diffraction gratings and crystal lattices produce sharp diffraction patterns from regularly spaced structures. What determines whether you'd use visible light or X-rays, and which equation governs crystal diffraction?