Episode 321: Interference patterns

When two or more waves meet, we may observe interference effects. It is likely that your students will have already met the basic ideas of constructive and destructive interference.

Lesson Summary

• Demonstrations: Simple interference phenomena (20 minutes)
• Demonstration: Two sound sources (15 minutes)
• Demonstration: Young’s two-slit experiment (15 minutes)
• Discussion: Deriving and using the formula (20 minutes)
• Student experiments: Double slit analogues (30 minutes)
• Student questions: Using the Young’s slits formula (40 minutes)
• Demonstrations: For students to explain (20 minutes)

The following simple demonstrations could be used to introduce this section; don’t feel that you have to give detailed explanations at this stage.

• Laser speckle pattern. Shine a laser onto a screen. Move your head side to side and observe the dark and light speckles, due to the different path lengths to the eye from different positions on the spot of laser light (If the beam is too small to show the speckles, try expanding it by passing it through a low-power lens, either converging or diverging.)
• Observe the colours in soap bubbles or oil films. Light is partly reflected by the upper surface of the film, partly by the lower surface. Depending on the thickness of the film, these two light rays will superpose constructively or destructively, depending on the wavelength. Thus two paths giving constructive superposition at one wavelength will not give constructive superposition for other wavelengths – hence only the colour with the correct wavelength is seen.
• Tuning forks. Hold the vibrating fork with its prongs vertical and close to the ear. Twist the fingers so the fork slowly rotates about a vertical axis. The loudness of the sound will rise and fall, four times per complete rotation. (Each prong acts as a source of sound waves; twisting the fork alters the distance between each prong and the eardrum.)

Emphasise that, in each case, there are two or more sources of light or sound reaching the eye or ear. You are going to look at an experiment designed to have two sets of light waves meeting in a very controlled way, i.e. Young’s two-slit experiment.

Safety

In any work with lasers, it is worth pointing out to the class the label in the laser. It should say Class 2: do not stare down the beam. With such a laser, a momentary reflection of the beam into someone’s eye will not cause an injury.

Demonstration: Two sound sources

Because the wavelength of light is very small, it is worth setting up an equivalent experiment with sound waves. Use two loudspeakers connected to a single signal generator. At this stage, it is not necessary to make detailed measurements.

Episode 321-1: Hearing superposition (Word, 84 KB)

Demonstration: Young’s two-slit experiment

Young’s two-slit experiment is perhaps one of the most famous experimental arrangements in physics. It was inspired by Young’s discovery of interference that he related in May 1801: Given a pond with a canal connected to it. At two places in the pond waves are excited. In the canal two waves superpose forming a resultant wave. The amplitude of the resultant wave is determined by the phase difference with which the two waves arrive at the canal.

Shine laser light through a double slit on to a screen. You should see a series of evenly-spaced bright spots (fringes or maxima). Ask students to relate this to the sound experiment. (The bright fringes are the equivalent of the loud points in the sound field.)

Point to the central bright fringe. Emphasise that two light rays reach this point, one from each slit. They have travelled the same distance, so there is no path difference between them. They started off in step (in phase) with each other, and now they arrive at the screen in phase with each other. Hence their displacements add up to give a brighter ray.

The next bright fringes (on either side of the central one) represent points where one ray has travelled λ further than the other, so they are back in phase. Why is there a dark fringe in between? (One ray has travelled λ/2 further than the other, so they are out of phase and interfere destructively.)

If we could measure these distances approximately, we could determine λ .

Show the effects of:

• Using two slits with a smaller separation (the fringes are further apart).
• Moving the screen closer to the slits (the fringes are closer together).

It is clear that we might use this experiment to determine the wavelength of light, but how?

A modern version of the Young’s Two Slit experiment was voted the most beautiful experiment in physics in a Physics World readers’ poll in 2002. It still forms the basis of ongoing research into the fundamental quantum nature of matter.

If you have already covered the photon model for light, you may want to refer back to this. As early as 1909, it was established that fringes were found even if the source was so faint that only one photon at a time was in the apparatus. Fringes can also be seen using de Broglie (or matter) waves. The most massive particles used to generate fringes to date (March 2005) are fluorinated buckyballs C₆₀F₄₈ (i.e. 1632 mass units).

Discussion: Deriving and using the formula

Now derive or quote the formula (depending upon your specification). A good way to start is to ask your students to identify the important variables (they are all lengths), and to give their approximate sizes:

λ , wavelength of the light (~500 nm)

d, separation of the two slits (~1 mm)

s, separation of the fringes (bright to bright or dark to dark) (~1 mm)

L, distance between slits and screen (~1 m)

How can we make a balanced equation from four quantities that are so different in magnitude? The simplest solution is that the product of the biggest and smallest is equal to the product of the two in-between quantities. Hence:

λ L = sd

or

λ d = sL

Episode 321-2: Calculating wavelength in two-slit interference (Word, 79 KB)

Episode 321-3: Two-slit interference (Word, 51 KB)

Student experiments: Double slit analogues

Set up a circus of Young’s two-slit arrangements (depending upon the available equipment to hand) using light, microwaves, 3GHz radio waves, ultra-sound (less noisy than audible sound!) and a ripple tank, and get students to determine the wavelength of the waves being used in each case.

You may prefer to set some up as demonstrations.

Episode 321-4: Interference patterns in a ripple tank (Word, 48 KB)

Episode 321-5: Measuring the wavelength of laser light (Word, 42 KB)

Student questions: sing the Young’s slits formula

The first set of questions covers the principles of Young’s experiment.

The second set is questions for practice in using the equation.

Episode 321-6: Questions on the two-slit experiment (Word, 28 KB)

Episode 321-7: Two-source interference: some calculations (Word, 23 KB)

Demonstration: For students to explain

Here are two fun demonstrations to round off this episode. Demonstrate them, and ask your students to provide explanations.

1. A nice demo using audible sound is to fix two loudspeakers at each end of a longish piece of wood. Mount the wood on a suitable pivot (large nail) mid-way between the two speakers. Drive both in parallel from signal generator. Slowly scan the class. As the interference fringes sweep across the audience, they hear the regular change in volume.
2. Make a sound trombone. Mount a small loudspeaker in the wide end of a small plastic funnel. Tubing from the other end divides into two tubes: one takes a direct route, the other a route whose length can be varied by a U-shaped glass tube sliding trombone section. The two routes combine and are fed into another funnel that acts as an earpiece.
The loudness of the sound depends upon the position of the trombone slider. It is obvious that there are two paths by which the sounds reach the ear. There may be a path difference between them. If the path lengths differ by an exact number of wavelengths, constructive interference increases the volume; integral half wavelength path differences mute the sound due to destructive interference. Do not confuse this with beats; here, only one frequency is involved, whereas beating is an effect due to two close frequencies (see below).