IGCSE Physics 0625

3.1 General properties of waves

Objective: Describe how wavelength affects diffraction at an edge

This section explores the phenomenon of diffraction, specifically focusing on how the wavelength of a wave influences the bending of waves as they pass around an obstacle or through an opening. We will examine diffraction at an edge and understand the relationship between wavelength and the extent of bending.

Diffraction

Diffraction is the bending of waves around obstacles or through openings. It's a wave property that distinguishes waves from particles. The amount of diffraction depends on the wavelength of the wave, the size of the obstacle or opening, and the distance from the obstacle or opening to the point where the wave is observed.

Diffraction at an Edge

When a wave encounters an edge, it doesn't simply stop or change direction abruptly. Instead, the wave continues to propagate, bending around the edge. This bending is called diffraction. The extent of diffraction is related to the wavelength of the wave.

How Wavelength Affects Diffraction at an Edge

The relationship between wavelength and diffraction is crucial. Longer wavelengths diffract more than shorter wavelengths. This means that waves with longer wavelengths will bend more significantly around an edge compared to waves with shorter wavelengths.

Consider the following:

• Long Wavelengths: Longer wavelengths have a greater ability to spread out and bend around obstacles. The wave fronts will spread more significantly, resulting in a wider spread of the wave after passing the edge.
• Short Wavelengths: Shorter wavelengths are less prone to diffraction. They tend to travel in a more straight line and the bending around the edge will be less pronounced.

This difference in diffraction is often quantified by the concept of diffraction angle. The diffraction angle is the angle between the original direction of the wave and the direction of the diffracted wave.

Mathematical Relationship (Simplified)

The amount of diffraction is related to the wavelength ($ \lambda $ ) and the size of the obstacle ($ a $ ) or opening ($ d $ ) by the following approximate formula (for single-slit diffraction, which is a related concept):

$$ \sin \theta = m \frac{\lambda}{a} $$

Where:

• $ \theta $ is the angle of diffraction.
• $ \lambda $ is the wavelength of the wave.
• $ a $ is the width of the obstacle or opening.
• $ m $ is an integer (1, 2, 3, ...), representing the order of the diffraction pattern.

This formula shows that as the wavelength ($ \lambda $ ) increases, the angle of diffraction ($ \theta $ ) also increases. Therefore, longer wavelengths lead to greater diffraction angles.

Examples

1. Water Waves: You can observe diffraction when water waves pass through a narrow gap or around a barrier. Longer water waves will spread out more noticeably than shorter ones.
2. Sound Waves: Sound waves also diffract. This is why you can hear someone speaking around a corner, even if you can't see them. The longer wavelengths of sound allow them to bend around obstacles.

Summary

In summary, the wavelength of a wave significantly affects its diffraction at an edge. Longer wavelengths diffract more than shorter wavelengths, resulting in a greater bending of the wave around the obstacle or opening. This is a fundamental property of waves and has important implications in various applications, from sound propagation to optical instruments.

Property	Effect on Diffraction
Wavelength (λ)	Longer wavelength leads to greater diffraction.
Size of Obstacle/Opening (a/d)	Smaller obstacle/opening leads to greater diffraction.