Describe how wavelength affects diffraction at an edge

Cambridge IGCSE Physics 0625 – Topic 3.1: General Properties of Waves

Objective

Describe how the wavelength of a wave influences the amount of diffraction that occurs when the wave encounters an edge or a narrow opening.

Key Concepts

• Diffraction – the bending and spreading of a wave as it passes an obstacle or through an aperture.
• Wavelength (λ) – the distance between successive points of equal phase in a wave (e.g., crest‑to‑crest).
• Characteristic size of the obstacle/aperture (a) – the width of the edge, slit, or opening that the wave encounters.

Relationship Between Wavelength and Diffraction

The extent of diffraction depends on the ratio of the wavelength to the size of the obstacle or opening. This relationship can be expressed qualitatively as:

• If λ ≈ a, the wave diffracts strongly and spreads widely.
• If λ < a, diffraction is weak; the wave continues mostly in a straight line.
• If λ > a, the wave may be almost completely blocked, but the portion that passes will diffract very broadly.

For a single slit or edge, the first‑order diffraction minimum occurs when

\$\$

a \sin \theta = m\lambda \qquad (m = 1,2,3,\dots)

\$\$

where θ is the angle measured from the original direction of propagation. A larger wavelength gives a larger angle θ, meaning more pronounced spreading.

Qualitative Description

1. Long wavelength (large λ)

   • The wave “feels” the edge as a relatively small perturbation.
   • Result: the wave bends around the edge and spreads out over a wide angular region.
   • Example: Radio waves (λ ≈ 1 m) diffract around buildings and hills.

2. Short wavelength (small λ)

   • The edge is large compared with the wave’s size.
   • Result: the wave is only slightly disturbed and proceeds almost straight ahead.
   • Example: Visible light (λ ≈ 500 nm) shows little diffraction at a door frame.

Practical Implications

• Design of communication systems – lower‑frequency (long‑wave) signals are chosen for long‑range transmission because they diffract around obstacles.
• Optical instruments – to obtain sharp images, apertures are made much larger than the wavelength of visible light to minimise diffraction blur.
• Acoustic engineering – low‑frequency sounds (long λ) can be heard around corners, whereas high‑frequency sounds are more directional.

Summary Table