IGCSE Physics 0625

3.1 General properties of waves

Objective: Describe how wavelength and gap size affects diffraction through a gap

Diffraction is the bending of waves as they pass through an obstacle or an opening. This phenomenon is a characteristic property of waves, particularly noticeable when the size of the obstacle or opening is comparable to the wavelength of the wave.

Diffraction through a Gap

When a wave encounters a gap, it will spread out beyond the gap as it passes through. The amount of spreading depends on the wavelength of the wave and the size of the gap.

Effect of Wavelength on Diffraction

The relationship between wavelength and diffraction is crucial.

• Longer Wavelengths: Waves with longer wavelengths (e.g., radio waves) diffract more significantly. They bend around obstacles and spread out more widely.
• Shorter Wavelengths: Waves with shorter wavelengths (e.g., X-rays) diffract less. They tend to travel in a more straight line and the diffraction effect is less pronounced.

Effect of Gap Size on Diffraction

The size of the gap relative to the wavelength of the wave determines the extent of diffraction.

There are two main scenarios:

• Gap Size > Wavelength: When the gap is larger than the wavelength of the wave, the wave will diffract significantly. The bending of the wave will be considerable, and the diffracted waves will spread out over a wider area.
• Gap Size < Wavelength: When the gap is smaller than the wavelength of the wave, the diffraction will be less pronounced. The wave will still bend slightly, but the spreading will be minimal.

Mathematical Relationship (Approximation)

The amount of diffraction can be approximated using the concept of the first minimum in diffraction. For a single slit, the angle to the first minimum is given by:

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

Where:

• $\theta$ is the angle to the first minimum.
• $\lambda$ is the wavelength of the wave.
• $a$ is the width of the gap.

From this equation, we can see that as the gap size ($a$) decreases (and assuming $\lambda$ remains constant), the angle $\theta$ increases, indicating greater diffraction.

Summary Table

Property	Effect on Diffraction
Wavelength	Longer wavelength leads to more diffraction. Shorter wavelength leads to less diffraction.
Gap Size	Gap size greater than wavelength leads to significant diffraction. Gap size less than wavelength leads to less diffraction.