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

Objective

Describe how a ripple tank can be used to demonstrate:

1. Reflection at a plane surface
2. Refraction caused by a change in speed due to a change in depth
3. Diffraction through a narrow gap
4. Diffraction around a straight edge

Apparatus

• Ripple tank with transparent sides and a smooth bottom
• Adjustable water depth control (e.g., a removable plate)
• Two point sources (or a single source with a movable barrier)
• Plane reflecting barrier (e.g., a glass plate)
• Rectangular slit of variable width
• Straight edge (e.g., a thin metal strip)
• Overhead projector or camera to view the wave pattern

General Procedure for All Demonstrations

1. Fill the tank with water to a uniform depth (typically 1–2 cm).

2. Generate a continuous, low‑frequency wave using a vibrator or a gently oscillating source.

3. Observe the wave fronts on the illuminated surface of the water.

4. Record the pattern qualitatively (sketches) and, where possible, measure distances between successive wave crests to determine wavelength \$λ\$.

Demonstration (a): Reflection at a Plane Surface

Setup: Place a vertical glass plate in the tank so that it forms a plane boundary perpendicular to the incident wave fronts.

1. Generate plane wave fronts that travel towards the plate.
2. Observe the incident and reflected wave fronts.

Observations

• The incident wave fronts approach the plate at an angle \$θ_i\$.
• After striking the plate, a set of reflected wave fronts emerges on the same side of the normal.
• The angle of reflection \$θr\$ equals the angle of incidence \$θi\$ (law of reflection).

\$θi = θr\$

Demonstration (b): Refraction Due to a Change in Depth

Setup: Create a step in the tank floor so that one half of the tank has a shallow depth \$d1\$ and the other half a deeper depth \$d2\$ (e.g., \$d1 = 0.5\,\$cm, \$d2 = 2\,\$cm).

1. Generate wave fronts that travel from the shallow region toward the deeper region at an oblique angle.
2. Observe the change in direction as the waves cross the depth boundary.

Observations

• Wave speed \$v\$ is greater in deeper water: \$v = \sqrt{g d}\$ (for shallow‑water waves, \$g\$ = acceleration due to gravity).
• The wavelength increases in the deeper region while the frequency \$f\$ remains constant.
• The wave front bends towards the normal when entering the shallower region and away from the normal when entering the deeper region.

Snell’s law for waves:

\$\frac{\sin θ1}{\sin θ2} = \frac{v1}{v2} = \frac{λ1}{λ2}\$

Demonstration (c): Diffraction Through a Narrow Gap

Setup: Place a rectangular slit of width \$a\$ in a barrier within the tank. Choose \$a\$ comparable to the wavelength \$λ\$ (e.g., \$a ≈ λ\$).

1. Direct a plane wave toward the slit.
2. Observe the pattern on the far side of the slit.

Observations

• If \$a \gg λ\$, the wave emerges with little spreading (geometrical optics limit).
• If \$a \approx λ\$, the wave spreads out into a circular (or semicircular) pattern – classic diffraction.
• The intensity of the diffracted wave decreases with increasing angle from the central axis.

Demonstration (d): Diffraction Around a Straight Edge

Setup: Position a thin, straight barrier (edge) in the path of the incident wave front.

1. Generate a plane wave that strikes the edge.
2. Observe the wave pattern on the far side of the edge.

Observations

• Behind the edge, the wave fronts bend around the tip, forming a series of curved fronts.
• The effect is most pronounced when the wavelength is comparable to the dimensions of the edge (i.e., the edge thickness is small compared with \$λ\$).
• The region directly behind the edge shows reduced amplitude (shadow region) but is not completely dark because of diffraction.

Summary Table

Key Points for Examination

• Identify the experimental arrangement that produces each effect.
• State the relationship between wave speed, depth, and wavelength for water waves.
• Explain why diffraction is most noticeable when the obstacle size is of the order of the wavelength.
• Use the correct terminology: incident wave, reflected wave, refracted wave, diffracted wave, normal, angle of incidence, etc.