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

In this section we consider three ways in which a wave can change direction or shape when it encounters a different medium or an obstacle:

1. Reflection at a plane surface
2. Refraction due to a change of speed
3. Diffraction through a narrow gap

a) Reflection at a plane surface

When a wave reaches a smooth, flat (plane) boundary it is reflected back into the original medium. The law of reflection states that the angle of incidence equals the angle of reflection:

\$\thetai = \thetar\$

Key points:

• The incident ray, the reflected ray and the normal to the surface all lie in the same plane.
• The reflected wave has the same speed, frequency and wavelength as the incident wave (provided the medium on the incident side does not change).
• If the reflecting surface is a good conductor for electromagnetic waves, the reflected wave may undergo a phase change of \$180^\circ\$ (a sign reversal).

b) Refraction due to a change of speed

When a wave passes from one medium into another where its speed is different, the wave changes direction. This bending is called refraction. The relationship between the angles and the speeds is given by:

\$\frac{\sin\theta1}{\sin\theta2} = \frac{v1}{v2}\$

where:

• \$\theta_1\$ = angle of incidence (measured from the normal in the first medium)
• \$\theta_2\$ = angle of refraction (measured from the normal in the second medium)
• \$v1\$, \$v2\$ = wave speeds in the first and second media respectively

Because \$v = f\lambda\$, the wavelength also changes while the frequency \$f\$ remains constant:

\$\lambda2 = \frac{v2}{f} = \lambda1\frac{v2}{v_1}\$

Typical examples:

• Light passing from air into water (speed decreases, ray bends towards the normal).
• Sound moving from air into a denser medium such as water (speed increases, ray bends away from the normal).

c) Diffraction through a narrow gap

Diffraction is the spreading of a wave as it passes an obstacle or aperture whose size is comparable to the wavelength. For a single narrow gap of width \$a\$ the main condition for noticeable diffraction is:

\$a \lesssim \lambda\$

When \$a\$ is much larger than \$\lambda\$, the wave emerges with little change in direction. When \$a\$ is comparable to or smaller than \$\lambda\$, the wave spreads out into a fan‑shaped pattern.

Key observations:

• The amount of spreading increases as the gap becomes narrower relative to the wavelength.
• Diffraction is more pronounced for longer wavelengths (e.g., radio waves diffract around buildings, while visible light diffracts only through very small slits).
• In a double‑slit arrangement, diffraction from each slit interferes, producing the classic interference pattern.

Summary table

Key equations to remember

• Wave speed: \$v = f\lambda\$
• Law of reflection: \$\thetai = \thetar\$
• Snell’s law (refraction): \$\displaystyle\frac{\sin\theta1}{\sin\theta2} = \frac{v1}{v2}\$
• Diffraction condition (single slit): \$a \lesssim \lambda\$

Understanding these three behaviours helps explain many everyday phenomena, from why we can see our reflection in a mirror to why radio signals can be received even when the transmitter is not in direct line‑of‑sight.