Describe how wavelength and gap size affects diffraction through a gap

3.1 General Properties of Waves – Diffraction Through a Gap

Diffraction Basics

When a wave encounters a gap of width $d$, the waves emerging from the gap spread out. The amount of spreading depends on the wavelength $\lambda$ and the size of the gap.

• Longer wavelengths (larger $\lambda$) diffract more.
• Smaller gaps (smaller $d$) also increase diffraction.
• When $\lambda \ll d$, diffraction is minimal – waves behave like straight rays.

Analogy: Water Ripples

Imagine a pond with a small stone creating ripples. If you put a narrow fence (gap) in the water, the ripples will bend around the fence. The larger the ripples (longer wavelength) or the narrower the fence (smaller gap), the more pronounced the bending. 🌊

Key Relationship

The first minimum in a single‑slit diffraction pattern occurs when:

For small angles, $\sin \theta \approx \theta$ (in radians), giving the simple approximation:

So, if you double the wavelength or halve the gap, the diffraction angle roughly doubles.

Quick Calculation Example

1. Wavelength of visible light: $\lambda = 500\,\text{nm}$
2. Gap width: $d = 1\,\text{mm}$
3. Approximate diffraction angle: $\theta \approx \dfrac{500\times10^{-9}\,\text{m}}{1\times10^{-3}\,\text{m}} = 5\times10^{-4}\,\text{rad}$
4. Convert to degrees: $5\times10^{-4}\,\text{rad} \times \dfrac{180^\circ}{\pi} \approx 0.029^\circ$

Table: Diffraction Angles for Different Gaps

Exam Tips

Summary

Diffraction is stronger when the wavelength is large compared to the gap size. The simple rule of thumb: $\theta \propto \lambda/d$. This relationship helps predict how waves will spread after passing through a narrow opening, a concept that appears in many physics exam questions.