Describe how wavelength and gap size affects diffraction through a gap

Published by Patrick Mutisya · 14 days ago

Cambridge IGCSE Physics 0625 – 3.1 General Properties of Waves: Diffraction through a Gap

3.1 General Properties of Waves

Objective

Describe how wavelength and gap size affect diffraction when a wave passes through a narrow opening.

What is Diffraction?

Diffraction is the bending and spreading of a wave as it encounters an obstacle or passes through an opening (a gap). The amount of spreading depends on the relationship between the wavelength (\$\lambda\$) of the wave and the characteristic dimension of the gap (\$a\$).

Key Relationship

For a single slit or narrow gap, the angular width (\$\theta\$) of the central diffraction maximum (for small angles) can be approximated by

\$\theta \approx \frac{\lambda}{a}\$

where:

  • \$\lambda\$ = wavelength of the incident wave
  • \$a\$ = width of the gap (or slit)
  • \$\theta\$ = angle between the central direction and the first minimum (in radians)

Effect of Wavelength

  • Longer wavelength (large \$\lambda\$): Increases \$\theta\$, producing a wider spread of the diffracted beam.
  • Shorter wavelength (small \$\lambda\$): Decreases \$\theta\$, so the beam remains more collimated.

Effect of Gap Size

  • Large gap (\$a \gg \lambda\$): \$\theta\$ becomes very small; diffraction is negligible and the wave passes almost straight through.
  • Gap comparable to wavelength (\$a \approx \lambda\$): \$\theta\$ is of order unity; noticeable spreading occurs.
  • Very narrow gap (\$a \ll \lambda\$): \$\theta\$ can become large (approaching \$90^\circ\$); the wave spreads in many directions.

Qualitative Summary Table

ConditionRelation of \$a\$ to \$\lambda\$Resulting DiffractionTypical Observation
Negligible diffraction\$a \gg \lambda\$Very small \$\theta\$ (beam stays narrow)Sharp shadow edge, little spreading
Moderate diffraction\$a \approx \lambda\$\$\theta \sim 1\$ radian (significant spread)Broad central maximum, visible side fringes
Strong diffraction\$a \ll \lambda\$Large \$\theta\$ (approaches \$90^\circ\$)Almost isotropic spreading, central maximum dominates

Practical Examples

  1. Visible light (\$\lambda \approx 500\,\$nm) passing through a slit of \$a = 5\,\$µm (\$a \approx 10\lambda\$) shows only slight diffraction.
  2. Radio waves (\$\lambda \approx 1\,\$m) encountering a doorway \$a = 1\,\$m produce a pronounced diffraction pattern, allowing the signal to bend around corners.
  3. Water waves with \$\lambda = 0.2\,\$m passing through a gap of \$a = 0.05\,\$m (\$a = 0.25\lambda\$) spread widely, creating a fan‑shaped pattern.

Important Points for Exam Answers

  • State the formula \$\theta \approx \lambda / a\$ and explain its meaning.
  • Compare the sizes of \$a\$ and \$\lambda\$ to predict whether diffraction will be strong, moderate, or weak.
  • Use real‑world examples to illustrate the concept.
  • Remember that the effect is the same for all types of waves (light, sound, water, etc.) as long as the wave nature is considered.

Suggested diagram: Sketch of a wavefront approaching a narrow gap, showing incident rays, the gap width \$a\$, and the diffracted rays spreading at angle \$\theta\$ on the other side.