Describe how waves can undergo: (a) reflection at a plane surface (b) refraction due to a change of speed (c) diffraction through a narrow gap

3.1 General Properties of Waves

Reflection at a Plane Surface

When a wave hits a flat surface, it bounces back. Think of a ball hitting a wall and rolling back in the opposite direction. For waves, the angle of incidence (the angle the incoming wave makes with the normal) equals the angle of reflection (the angle the reflected wave makes with the normal). 🎯

• Reflection occurs on any smooth surface.
• The wave energy is not lost; it just changes direction.
• Sound waves bounce off walls, creating echoes.
• Light waves reflect off mirrors, allowing us to see ourselves. 🔁

Refraction Due to a Change of Speed

When a wave passes from one medium to another (e.g., air to water), its speed changes, causing the wave to bend. This bending is called refraction. A common example is a straw appearing bent in a glass of water. 🌊

The relationship between the angles and the speeds (or refractive indices) is given by Snell’s Law:

\$ n1 \sin\theta1 = n2 \sin\theta2 \$

Where:

• n₁ and n₂ are the refractive indices of the first and second media.
• θ₁ is the angle of incidence.
• θ₂ is the angle of refraction.

If the wave slows down (n₂ > n₁), the wave bends toward the normal; if it speeds up, it bends away. 📐

Diffraction Through a Narrow Gap

Diffraction happens when a wave encounters an obstacle or passes through a slit that is comparable in size to its wavelength. Imagine a pond with a small crack in the shore; the ripples spread out on the other side, creating a fan‑shaped pattern. 🌊🔍

1. Wavefronts hit the slit.
2. Each point on the slit acts as a new source of waves.
3. These secondary waves interfere, producing bright and dark fringes.

In a single‑slit experiment with light, the intensity pattern on a screen can be described by:

\$ I(\theta) = I_0 \left( \frac{\sin(\beta)}{\beta} \right)^2, \quad \beta = \frac{\pi a \sin\theta}{\lambda} \$

Where a is the slit width and λ is the wavelength. The central maximum is the brightest, with progressively dimmer side maxima. 🎨