show an understanding of experiments that demonstrate diffraction including the qualitative effect of the gap width relative to the wavelength of the wave; for example diffraction of water waves in a ripple tank

Diffraction

Definition (Cambridge 9702 wording): Diffraction is the bending and spreading of a wave when it encounters an obstacle or an aperture whose dimensions are comparable to the wavelength of the wave.

1. Qualitative description – how the aperture size relates to the wavelength

• a ≫ λ – the aperture is much larger than the wavelength. The wave emerges almost unchanged; only a very small amount of spreading is seen at the edges.
• a ≈ λ – the aperture size is of the same order as the wavelength. Noticeable bending occurs and the wavefronts behind the aperture become curved.
• a ≪ λ – the aperture is much smaller than the wavelength. The opening acts like a point source and the wave spreads uniformly in all directions.

2. Experiments that demonstrate diffraction

All four experiments listed in the syllabus are described below. A short note on the distinction between diffraction (single‑aperture) and interference (multiple‑aperture) is included, as the syllabus treats them as separate sub‑topics.

2.1 Single‑slit light diffraction (diffraction experiment)

• Setup: A monochromatic laser (or a collimated white‑light source with a narrow band‑pass filter) is aimed at a single slit of width a.
• Observation: On a screen a bright central maximum is seen with a series of weaker side maxima (the classic diffraction pattern).
• Link to theory: The positions of the minima satisfy a sin θ = mλ (m = ±1, ±2,…).

2.2 Double‑slit (Young’s) experiment (interference experiment)

• Setup: Two parallel slits separated by distance a are illuminated by coherent light.
• Observation: A regular series of bright and dark fringes appears on a distant screen.
• Qualitative difference: The pattern is primarily due to interference of two coherent sources; diffraction of each individual slit merely modulates the envelope of the fringes.
• Geometric relationship (syllabus form):

  \[

  \lambda = \frac{a\,x}{D}

  \]

  where x is the fringe spacing measured on the screen and D is the distance from the slits to the screen.

• Principal‑maxima condition (often quoted for double‑slit or grating):

  \[

  a\sin\theta = n\lambda \qquad (n = 0,\pm1,\pm2,\dots)

  \]

2.3 Diffraction grating (many‑slit diffraction)

• Setup: A transmission grating with groove spacing d is illuminated by monochromatic light.
• Observation: Sharp, well‑separated spectral orders appear on a screen.
• Grating equation:

  \[

  d\sin\theta = n\lambda \qquad (n = 0,\pm1,\pm2,\dots)

  \]

  The number of illuminated grooves N determines the sharpness and intensity of the maxima but does not appear in the basic equation required by the syllabus.

2.4 Ripple‑tank demonstration (water‑wave diffraction)

A point source generates circular water waves that strike a barrier containing a rectangular gap of width a. Three regimes are observed, illustrating the qualitative effect of the ratio a/λ:

3. Quantitative relationships required by the syllabus

• Single‑slit minima: \[

  a\sin\theta = m\lambda \qquad (m = \pm1,\pm2,\dots)

  \]

• Double‑slit (interference) – geometric form: \[

  \lambda = \frac{a\,x}{D}

  \]

  where a is the slit separation, x the fringe spacing on the screen, and D the screen‑slit distance.

• Double‑slit (or grating) principal maxima: \[

  a\sin\theta = n\lambda \qquad (n = 0,\pm1,\pm2,\dots)

  \]

• Diffraction grating: \[

  d\sin\theta = n\lambda \qquad (n = 0,\pm1,\pm2,\dots)

  \]

4. Connection to optical resolution

Diffraction limits the smallest angular separation θ that an optical instrument can resolve. For a circular aperture of diameter D, the Rayleigh criterion gives

\[

\theta_{\text{min}} \approx 1.22\frac{\lambda}{D}.

\]

This explains why telescopes, microscopes and cameras cannot distinguish details finer than the diffraction limit.

5. Practical applications

1. Design of telescopes, microscopes and camera lenses – accounting for the diffraction limit.
2. Acoustic engineering – predicting how sound diffracts through doors, windows and perforated panels.
3. Coastal and marine engineering – assessing the effect of sea‑walls, breakwaters and harbour entrances on water‑wave diffraction.
4. Spectroscopy – using diffraction gratings to separate light into its constituent wavelengths.

6. Summary

Diffraction provides clear experimental evidence of the wave nature of light, sound, water waves and many other phenomena. By varying the size of an aperture relative to the wavelength, the transition from almost straight‑line propagation (a ≫ λ) to complete spreading (a ≪ λ) can be observed. The core quantitative relationships required by the Cambridge IGCSE/A‑Level Physics syllabus are:

• Single‑slit minima: a sin θ = mλ
• Double‑slit (interference) geometric form: λ = a x / D
• Double‑slit or grating principal maxima: a sin θ = nλ (or d sin θ = nλ for a grating)

Understanding these concepts and the associated experiments equips students to tackle both the qualitative and quantitative aspects of diffraction in the Cambridge syllabus.