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

Published by Patrick Mutisya · 14 days ago

Cambridge A-Level Physics 9702 – Diffraction Notes

Diffraction

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. The phenomenon is a direct consequence of the wave nature of light, sound, water waves, etc.

Key Concepts

  • The amount of bending increases as the size of the aperture (or obstacle) becomes closer to the wavelength \$\\lambda\$.

  • When the aperture is much larger than \$\\lambda\$, the wave propagates almost straight with little spreading.

  • When the aperture is much smaller than \$\\lambda\$, the wave spreads uniformly in all directions (approaching a point source).

Mathematical Description (Single‑Slit Approximation)

The condition for the first minimum in a single‑slit diffraction pattern is

\$a \sin\theta = \lambda\$

where \$a\$ is the slit width, \$\\theta\$ the angle measured from the central axis, and \$\\lambda\$ the wavelength.

Experiments Demonstrating Diffraction

1. Single‑Slit Light Diffraction

A monochromatic laser beam passes through a narrow slit and projects a pattern of a bright central maximum flanked by weaker side maxima on a screen.

Suggested diagram: Laser beam → narrow slit → diffraction pattern on screen.

2. Double‑Slit Interference (Young’s Experiment)

Two parallel slits act as coherent sources. The resulting pattern shows alternating bright and dark fringes whose spacing depends on slit separation \$d\$ and wavelength \$\\lambda\$:

\$d \sin\theta = m\lambda \qquad (m = 0, \\pm1, \\pm2, …)\$

Suggested diagram: Two slits illuminated by a laser, producing an interference pattern.

3. Diffraction Grating

A grating contains many equally spaced slits. The condition for principal maxima is

\$N d \sin\theta = m\lambda\$

where \$N\$ is the number of illuminated slits. Gratings give very sharp, well‑separated spectral lines.

Suggested diagram: Light incident on a diffraction grating, showing multiple orders.

4. Ripple Tank – Water‑Wave Diffraction

A ripple tank provides a visual demonstration of diffraction with water waves. A point source generates circular wavefronts that encounter a barrier with a gap of width \$a\$.

  • Gap width \$a \gg \lambda\$: Waves pass through with little change; the transmitted wavefronts remain approximately planar.

  • Gap width \$a \approx \lambda\$: Noticeable spreading occurs; the wavefronts become semicircular behind the gap.

  • Gap width \$a \ll \lambda\$: The gap acts as a point source; waves radiate outward in all directions, forming concentric circles.

Suggested diagram: Ripple tank with a barrier containing a variable‑width gap, showing three regimes of diffraction.

Qualitative Effect of Gap Width Relative to Wavelength

The relationship between the gap width \$a\$ and the wavelength \$\\lambda\$ determines the diffraction pattern. The table below summarises the observable behaviour.

Ratio \$a/\\lambda\$Observed DiffractionTypical Pattern
\$a/\\lambda \\gg 1\$Minimal bending; wavefronts remain essentially straight.Sharp, well‑defined beam; small side fringes (if any).
\$a/\\lambda \\approx 1\$Significant bending; wavefronts spread noticeably.Broad central maximum with visible side lobes.
\$a/\\lambda \\ll 1\$Strong bending; aperture behaves like a point source.Nearly circular wavefronts; intensity falls off isotropically.

Practical Applications

  1. Design of optical instruments (e.g., telescopes, microscopes) where diffraction limits resolution.

  2. Acoustic engineering – controlling sound propagation through openings.

  3. Water‑wave studies – coastal engineering and wave‑energy devices.

  4. Diffraction gratings in spectrometers for wavelength analysis.

Summary

Diffraction illustrates the wave nature of physical phenomena. By varying the size of an aperture relative to the wavelength, one can observe a continuum from straight‑line propagation to complete spreading. Experiments such as the single‑slit, double‑slit, diffraction grating, and ripple‑tank demonstrations provide clear, observable evidence of these effects, forming a cornerstone of the A‑Level Physics curriculum.