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
Condition
Relation of \$a\$ to \$\lambda\$
Resulting Diffraction
Typical 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
Visible light (\$\lambda \approx 500\,\$nm) passing through a slit of \$a = 5\,\$µm (\$a \approx 10\lambda\$) shows only slight diffraction.
Radio waves (\$\lambda \approx 1\,\$m) encountering a doorway \$a = 1\,\$m produce a pronounced diffraction pattern, allowing the signal to bend around corners.
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.