Describe the use of a ripple tank to show: (a) reflection at a plane surface (b) refraction due to a change in speed caused by a change in depth (c) diffraction due to a gap (d) diffraction due to an edge

3.1 General Properties of Waves – Ripple‑Tank Demonstrations

Link to Cambridge IGCSE/A‑Level Syllabus (Physics 3.1)

• Wave definition and energy transfer
• Transverse vs longitudinal waves
• Wave‑speed relationships: v = fλ, v = √(gd) (water), v = √(T/μ) (string – not required for the tank but useful for the syllabus)
• Reflection, refraction, diffraction (gap and edge)
• Super‑position & interference (briefly mentioned as the basis of diffraction)
• Application of Huygens’ principle

Learning Objectives

• Define a wave and explain how it transports energy without transporting matter.
• Distinguish transverse and longitudinal waves and give one everyday example of each.
• Identify the apparatus needed to demonstrate reflection, refraction, and the two types of diffraction in a ripple tank.
• Use the equations v = fλ, v = √(gd) (and, where appropriate, v = √(T/μ)) to calculate wave speed and wavelength from experimental data.
• Apply Huygens’ principle to explain why diffraction occurs.
• Interpret the observed patterns in terms of the law of reflection, Snell’s law for water waves, and the single‑slit diffraction condition.
• Relate laboratory observations to real‑world technologies (e.g., sonar, medical ultrasound, optical resolution).

Key Concepts

• Wave: a periodic disturbance that transfers energy from one point to another while the medium’s particles oscillate about an equilibrium position.
• Transverse wave: particle motion is perpendicular to the direction of propagation (water‑surface waves, light).
• Longitudinal wave: particle motion is parallel to the direction of propagation (sound in air, pressure waves in a stretched string).

Wave‑speed formulas (syllabus‑relevant)

Glossary of Symbols & Terms

Apparatus (common to all four demonstrations)

• Ripple tank with transparent sides and a level, smooth bottom.
• Depth‑control plate (removable or adjustable) for creating steps.
• Mechanical vibrator or electronic oscillator (frequency range 2–10 Hz).
• Overhead projector or digital camera to project the illuminated surface onto a screen.
• Calibrated grid or ruler placed beneath the tank for measuring λ.

Specific items for each phenomenon

• Reflection: vertical plane glass plate (smooth, flat).
• Refraction: stepped bottom giving two depths d₁ and d₂.
• Diffraction (gap): rectangular slit of adjustable width a (e.g., a = 0.5 λ, λ, 2 λ).
• Diffraction (edge): thin straight metal strip (edge thickness ≪ λ).

General Procedure (applies to all set‑ups)

1. Set the water depth to the required value (usually 1–2 cm; adjust for the refraction step).
2. Turn on the vibrator and tune the frequency until clear, evenly spaced wavefronts are produced.
3. Place the appropriate obstacle (plate, step, slit, or edge) in the path of the incident wavefronts.
4. Project the pattern onto a screen and sketch the wavefronts directly on the image.
5. In a region where the fronts are straight, measure the distance between successive crests to obtain λ.
6. Record the oscillator frequency f and calculate the speed using v = fλ.
7. For refraction, also record the depths d₁ and d₂ to compare with v = √(gd).

Demonstration (a): Reflection at a Plane Surface

Setup

• Insert the vertical glass plate so its surface is perpendicular to the incident wavefronts.
• Adjust the source to produce nearly planar wavefronts that strike the plate.

Observations

• Incident wavefronts approach the plate at an angle θ_i.
• Reflected wavefronts emerge on the same side of the normal, making an angle θ_r.
• Measured angles satisfy θ_i = θ_r (law of reflection).

Worked Example

Measured λ = 2.0 cm, f = 5 Hz.

1. v = fλ = 5 × 0.020 = 0.10 m s⁻¹.
2. Using a protractor on the projected image, θ_i = 30° and θ_r = 30°, confirming the law.

Key Principle

Law of reflection: θ_i = θ_r (measured with respect to the normal).

Demonstration (b): Refraction Caused by a Change in Depth

Setup

• Place a removable plate to create a step: shallow side depth d₁ = 0.5 cm, deep side depth d₂ = 2.0 cm.
• Generate plane wavefronts that travel from the shallow region toward the deeper region at an oblique angle.

Observations

• Wave speed in shallow water: v₁ = √(g d₁) ≈ 0.22 m s⁻¹.
• Wave speed in deep water: v₂ = √(g d₂) ≈ 0.44 m s⁻¹.
• Because the frequency is unchanged, λ doubles when the wave enters the deeper region.
• Wavefronts bend away from the normal when entering the faster (deeper) region and toward the normal when entering the slower (shallower) region.

Derivation of Snell’s Law for Water Waves

1. For a given frequency f, λ = v/f in each region.
2. Continuity of the wave‑vector component parallel to the boundary gives k₁ sin θ₁ = k₂ sin θ₂, where k = 2π/λ.
3. Substituting k = 2πf/v yields (2πf/v₁) sin θ₁ = (2πf/v₂) sin θ₂ → sin θ₁ / sin θ₂ = v₁ / v₂.
4. Since v ∝ √d, the ratio can also be written sin θ₁ / sin θ₂ = √(d₁/d₂).

Snell’s Law (IGCSE form)

\$\frac{\sin\theta{1}}{\sin\theta{2}}=\frac{v{1}}{v{2}}=\frac{\lambda{1}}{\lambda{2}}=\frac{\sqrt{d{1}}}{\sqrt{d{2}}}\$

Worked Example

Measured angles: θ₁ = 35° (shallow) and θ₂ = 55° (deep).

1. sin 35° / sin 55° ≈ 0.574 / 0.819 ≈ 0.70.
2. Predicted speed ratio: √(d₁/d₂) = √(0.5/2.0) = 0.50.
3. The discrepancy highlights experimental errors (e.g., non‑sharp depth step, slight curvature of wavefronts).

Demonstration (c): Diffraction Through a Narrow Gap

Setup

• Insert a rectangular slit of width a in a vertical barrier.
• Test three widths: a ≫ λ, a ≈ λ, and a < λ.
• Direct a plane wave toward the slit.

Observations

Underlying Principle – Huygens’ Principle

Every point on the slit acts as a secondary source of circular wavelets. The new wavefront is the envelope of these wavelets, producing the observed spreading.

Quantitative Description (optional, for extension students)

For a single slit, intensity varies with angle θ as

\$\$I(\theta)\;\propto\;\left(\frac{\sin\beta}{\beta}\right)^{2},\qquad

\beta=\frac{\pi a\sin\theta}{\lambda}\$\$

The first minimum occurs when β = π → a sin θ = λ.

Worked Example

λ = 1.2 cm, a = 1.2 cm → first minimum at sin θ = λ/a = 1 → θ ≈ 90°. In practice a broad central maximum and weak side lobes are seen, illustrating limited resolution for a narrow aperture.

Demonstration (d): Diffraction Around a Straight Edge

Setup

• Place a thin vertical metal strip so its edge intercepts the incident wavefronts.
• Generate a plane wave that strikes the edge nearly normal to the surface.

Observations

• Behind the edge the wavefronts curve around the tip, forming a series of concentric arcs (Fresnel diffraction).
• A region of reduced amplitude (partial shadow) appears directly behind the edge, but it is not completely dark because secondary wavelets from points along the illuminated edge fill the region.
• The effect is most noticeable when the edge thickness ≪ λ.

Underlying Principle – Huygens’ Principle for an Edge

Every point on the illuminated part of the edge acts as a secondary source. The superposition of the resulting wavelets produces the curved fronts and the partial shadow.

Quantitative Estimate (extension)

The width of the first bright Fresnel zone behind an edge is roughly

\$w \;\approx\; \sqrt{\lambda D}\$

where D is the distance from the edge to the observation screen.

Worked Example

λ = 1.0 cm, D = 4 cm → w ≈ √(1.0 × 4) ≈ 2 cm, matching the observed width of the first bright fringe.

Assessment Tips for Teachers

• Ask candidates to sketch the reflected or refracted wavefronts and label the relevant angles.
• Include a short calculation: given depth d and frequency f, compute the expected λ and predict the direction of the refracted ray using Snell’s law.
• For diffraction, require a statement of Huygens’ principle and, where appropriate, the condition a sin θ = λ for the first minimum.
• Link the experiment to a real‑world example (e.g., why a lighthouse uses a large aperture to produce a narrow beam).

Summary Table of Observations and Principles