Reflection, refraction and diffraction of waves: WASSCE Physics

Waves bounce, bend and spread. You hear a friend talking round a corner, you see a straight stick look bent in water, and you hear your voice echo back from a hill. These are reflection, refraction and diffraction — behaviours shared by every kind of wave.

Learning objectives

By the end of this lesson you should be able to:

state the laws of reflection and describe the reflection of water waves
explain refraction as a change of speed and use $n = \dfrac{v_1}{v_2} = \dfrac{\lambda_1}{\lambda_2}$
describe diffraction and the effect of gap size
give everyday examples of each phenomenon for sound and light

Reflection

Definition

Reflection is the bouncing back of a wave when it strikes a barrier or a boundary between two media.

Laws of reflection:

The angle of incidence equals the angle of reflection.
The incident wave (ray), the reflected wave (ray) and the normal at the point of incidence all lie in the same plane.

In a ripple tank, straight waves hitting a straight barrier at an angle are reflected at the same angle. Circular waves from a point reflected by a straight barrier appear to come from an image point behind it, just like light in a plane mirror. The wavelength, frequency and speed are unchanged by reflection.

Examples: echoes of sound, light in mirrors, radar, water waves at a harbour wall.

Refraction

Definition

Refraction is the change in direction of a wave as it passes from one medium into another, caused by a change in its speed.

Straight water waves passing from deep water into shallow water: the wavefronts are closer together in the shallow water and the direction of travel bends towards the normal

Figure 1. Water waves slow down in shallow water and bend towards the normal. WASSCE Tutor diagram.

When water waves move from deep to shallow water:

their speed decreases
their wavelength decreases (the wavefronts get closer together)
their frequency stays the same
their direction bends towards the normal (unless they meet the boundary head-on)

The refractive index from medium 1 to medium 2 is

n = \dfrac{\sin i}{\sin r} = \dfrac{v_1}{v_2} = \dfrac{\lambda_1}{\lambda_2}

\begin{aligned}n &= \dfrac{\sin i}{\sin r} \\ &= \dfrac{v_1}{v_2} \\ &= \dfrac{\lambda_1}{\lambda_2}\end{aligned}

Worked example

Water waves of wavelength 3.0 cm travel at 15 cm s⁻¹ in deep water. In shallow water their speed is 10 cm s⁻¹. Find (a) their frequency, (b) their wavelength in shallow water.

(a) $f = \dfrac{v}{\lambda} = \dfrac{15}{3.0} = 5$ Hz (unchanged in both regions).

(b) $\lambda_2 = \dfrac{v_2}{f} = \dfrac{10}{5} = 2.0$ cm.

In Sierra Leone

Waves rolling towards Lumley Beach slow down as the water gets shallower near the shore. Their fronts swing round until they arrive almost parallel to the beach, whatever direction they came from out at sea. That is refraction.

Diffraction

Definition

Diffraction is the spreading out of waves as they pass through a gap (aperture) or round the edge of an obstacle.

Left: waves passing through a wide gap continue almost straight with little spreading. Right: waves passing through a narrow gap spread out in circular arcs

Figure 2. The narrower the gap compared with the wavelength, the more the waves spread. WASSCE Tutor diagram.

Diffraction is greatest when the gap is about the same size as the wavelength.
A gap much wider than the wavelength gives little diffraction.
Diffraction does not change the wavelength, frequency or speed.

Examples:

Sound (wavelengths about 0.3–3 m) diffracts round doorways and buildings, so you hear people you cannot see.
Light has a tiny wavelength (about $5 \times 10^{-7}$ m), so it diffracts only through very narrow slits; that is why light seems to travel in straight lines and casts sharp shadows.
Long-wave radio diffracts round hills, so it can be received in valleys; short-wave TV signals cannot, which is why some towns need relay masts.

Key points

Reflection: angle of incidence = angle of reflection; λ, f and v unchanged.
Refraction: change of direction due to change of speed; frequency unchanged; $n = \dfrac{v_1}{v_2} = \dfrac{\lambda_1}{\lambda_2} = \dfrac{\sin i}{\sin r}$ .
Diffraction: spreading through gaps and round obstacles; greatest when gap ≈ wavelength.

WASSCE examination focus

WAEC tests this

Expect to describe how a ripple tank shows reflection, refraction and diffraction, to draw wavefronts before and after a boundary or gap (keep the wavelength constant through a gap, shorter in shallow water), and to explain why sound is heard round corners but light is not. Calculations use $v = f\lambda$ with an unchanged frequency.

Quick check

Which quantity does not change when a wave is refracted?
When is diffraction at a gap greatest?
Why can you hear someone around a corner but not see them?

Answers: 1. The frequency. 2. When the width of the gap is about equal to the wavelength. 3. Sound waves have wavelengths comparable to doorways, so they diffract a lot; light's wavelength is far smaller, so it hardly diffracts.

Reflection, refraction and diffraction of waves

Learning objectives

Reflection

Refraction

Diffraction

Key points

WASSCE examination focus

Quick check

Keep going with wave phenomena

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