Describe how wavelength affects diffraction at an edge

3.1 General Properties of Waves – Diffraction at an Edge

What is Diffraction?

Diffraction is the bending and spreading of waves when they encounter an obstacle or pass through an opening. Think of a stone dropped in a pond – the ripples bend around the stone and continue to spread. 🌊

How Wavelength Influences Diffraction

The key factor is the ratio between the wavelength \$λ\$ and the size of the obstacle or opening, often denoted \$a\$. A simple rule of thumb is:

• When \$λ \gg a\$ (wavelength much larger than the obstacle), diffraction is strong – waves bend a lot.
• When \$λ \ll a\$ (wavelength much smaller than the obstacle), diffraction is weak – waves pass almost straight through.
• When \$λ \approx a\$, diffraction is noticeable but not extreme.

Mathematically, the approximate diffraction angle \$\theta\$ for a single edge can be expressed as:

\$\theta \approx \frac{λ}{a}\$

So, the larger the wavelength relative to the edge, the larger the angle of bending.

Real‑World Analogies

1. Water waves at a rock: A stone in a pond creates waves that bend around it. The longer the waves (e.g., low‑frequency ripples), the more they spread around the stone.
2. Sound around a doorway: A 500 Hz sound has a wavelength of about 0.68 m. It can bend around a small doorway, so you can hear music from the other side even if the door is closed. 🎧
3. Light through a slit: Visible light has wavelengths around 400–700 nm, far smaller than a typical doorway. Light hardly diffracts around a door, so you see a sharp shadow.

Summary Table

Key Takeaway

Diffraction becomes more pronounced as the wavelength \$λ\$ becomes larger relative to the size of the obstacle or opening \$a\$. This explains why you can hear music through a closed door (sound waves are long) but not see it (light waves are very short). Understanding this relationship helps predict how different waves behave in everyday situations. 💡