 # Reflection, Refraction, Diffraction & Interference...That's COOL!

The Mini Ripple Tank is a great way to address the wave-energy standards and to teach about the properties of waves by showing how water waves behave. This is in keeping with the history of physics and the modern experimental approaches to science instruction. The Mini Ripple Tank eliminates the clumsiness of the larger ripple tanks of old and gives the opportunity for students and teachers to interact with the wave properties quickly and engagingly. Because of the competitive price, and variety of available experiments. It is even reasonable to buy a class set.

Getting Familiar

The Mini Ripple Tank contains a small pan for water and a vibrating source. The strobe light below projects waves of various frequencies on a fold-down screen. Both the strobe and the wave frequencies can be varied, generating many interesting effects. There is also a synchronizing mode which links the two (this is very helpful when measuring wavelength).

Figure 1. Water is filled up to half of the height. The adjustable strobe projects from underneath.

The device comes with three distinct wave generating mechanisms: single source, double source, and plane waves. The single source is the most fundamental and is helpful in instructing on wave basics and Huy gen's Principle (plane waves are a sum of circular waves). The double source can be used best at teaching interference experiments (more below) as well as testing out the diffraction formula. The plane wave source is the one I tend to use the most often because it sets up a standard wave that can readily land upon the other implements which are used to redirect the waves.

Figure 2. The nine components. Left to right: the two lenses and the prism, the two barriers and the parabolic mirror, and the double and single sources, as well as the plane wave source.

As for general tips, it is helpful to use a document camera for larger classes, also adding blue dye can sometimes improve visibility, and try to not overload the tank with water – either fill halfway or just enough to barely cover the lenses and prism. Experiment a lot with wave and strobe speeds to improve the visibility of the desired effects.

Refraction by the Lenses and the Prism

The bending of light waves by glass is well-known, but is this a property of all waves? Yes! Demonstrate this dramatically by bending water waves with lenses and prisms. The shallower the water, the slower the waves. This is analogous to the denser the medium, the slower the light waves (with few exceptions).

Figure 3. The prism can bend the waves by slowing their propagation.

Again, remember to keep the water shallow. Some experiments can include measuring the focal lengths of the two lenses (positive for convex, negative for concave), measuring the index of refraction for the prism (by wavelength change, speed change, or Snell's Law), and measuring how water depth affects refractive index.

n1 λ1 = n2 λ2

n = c/v

n1 sin θ1 = n2 sin θ2

The refraction formulas that can be used for quantitative experiments. The first formula might be the least familiar – wavelength changes with index of refraction. The second formula compares a standard speed c with the new slower one v to define the index n. The third is the famous Snell's Law.

Figure 4. The convex and concave lenses demonstrate convergence and divergence of waves respectively.

Figure 5. Reflection of plane waves off a parabolic mirror will focus them to a point.

Reflection by Barriers and the Parabolic Mirror

The law of reflection can be readily demonstrated by the Mini Ripple Tanks (by stacking the barrier pieces) however, the best demonstration is the focusing of waves by the parabolic mirror.

When a plane wave enters parallel to the axis of a parabolic mirror, it will be reflected to the focus of that mirror. This is the basis for Newtonian Reflector telescopes that remain the standard style in modern times. A reversal can also be achieved by placing the single source at the focal point and reflecting out plane waves.

Somehow it is very satisfying to see the focusing of water waves when using lenses. The ray approach to drawing images known as geometric optics does not provide a hypothesis as to the wave nature of light, but this experiment convincingly demonstrates that refraction and focusing is something that waves do! Refraction and lens effects are a powerful piece of evidence that demonstrates the wave nature of light.

Figure 6. Single slit diffraction shows the bending of a plane wave source as it passes through an opening, illustrating Huygen's Principle that plane waves are a sum of circular waves.

Diffraction by Barriers

Single-slit diffraction of waves is easily demonstrated with this simple device. Just place the barriers in the path of the plane wave source and the effect is immediately present. Manipulating the opening and wavelength can help illustrate the variables: more diffraction occurs the smaller the opening is allowed to be.

Figure 7. An interference pattern is easily generated with these two sources. The diffraction formulas above will apply to this double source interference pattern, even though no diffraction is occurring. This demonstration can be converted into a quantitative experiment.

The diffraction formula for quantitative experiments is best applied to the two-source case, however, and while this is only a case of interference and not diffraction, it does provide an opportunity to apply the formula experimentally.   Here, we see both versions of the formula, the angular version, and the small angle approximation. I prefer the second one because lengths are usually easier to measure than angles.

d sin θ = m λ

Xmm λ L/d

The diffraction formulas: The symbol d represents the distance between the sources, and lambda as always is wavelength (which is the dependent variable in this experiment). Theta is the angular distance to an interference fringe as measured from the spot half-way between the sources. X is the linear distance between the interference fringes, these are the locations of constructive interference. L is the linear distance from the point between the sources to the point of interest, and because there is more than one location of constructive interference, m is the index number which labels these points as m=1,0,-1,2, etc, (any integer).

January 10, 2019 Collin Wassilak