# Diffraction of a plane wave by multiple gaps

##### Demonstration

This ripple tank experiment models the action of a diffraction grating.

#### Apparatus and materials

Barriers, small

Barriers, large

Power supply, low voltage Continuously variable

Motor mounted on beam, with beam support

Light source, compact

#### Health & Safety and Technical notes

Beware of water on the laboratory floor. Make sure you have a sponge and bucket handy to mop up spills immediately.

Place the power supply for the lamp on a bench, not on the floor by the tank.

Photo-induced epilepsy
In all work with flashing lights, teachers must be aware of any student suffering from photo-induced epilepsy. This condition is very rare. However, make sensitive inquiry of any known epileptic to see whether an attack has ever been associated with flashing lights. If so, the student could be invited to leave the lab or shield his/her eyes as deemed advisable. It is impracticable to avoid the hazardous frequency range (7 to 15 Hz) in these experiments.

You need 2 large barriers and 6 small barriers.

Avoid very high motor speeds, which cause unwanted vibration of the barriers.

#### Procedure

a First set up the ripple tank with about 1 cm depth of water.

b Set up a line of small barriers 5 cm from the vibrator, as shown. There should be a gap of 2 to 3 cm between each.

c Start the motor at a low speed (4 rev/second).

Ask: Can you see semicircular ripples emerging from the gaps? Further out, can you see waves moving out in slanting directions, as well as a wave moving straight ahead?
Students should observe the interference pattern carefully, with and without stroboscopes.

Keeping the barriers arrangement the same, gradually increase the motor speed.
Ask: How does the interference pattern change?

#### Teaching notes

1 The pattern produced with multiple gaps is less clear than the double gaps experiment but, with care in aligning the gaps, it is visible. It will help if students have first seen diagrams of sets of semicircles to represent a snapshot of waves proceeding from several gaps.

The spacing of nodal lines will decrease as the wave frequency increases.

2 If students agree that the many gaps ‘grating’ produces circular waves in various directions, you can show them some simple geometry. Draw ‘rays’ from successive gaps to a diffracted plane wave-front and point out that the extra path when you change from one gap to the next is one wavelength for first order. Then the geometry is clear.

one wavelength / d = sin A

where d is the slit separation and A is the angle of deviation of the new wavefront from the direction of original beam.

3 You may want to make a direct comparison between this experiment and light striking a diffraction grating. If a beam of white light is a stream of waves, a wavelet must emerge from every illuminated gap of the grating. Since the gaps must be very narrow — because there are so many crowded together in the small grating – those wavelets must almost be semicircles. Look at them in the diagram and in the ripple tank.

same path lengths

If these wavelets continue out to a screen very far away, there will be places where the wavelets from all the gaps arrive in step. In the central bright image all those contributions have the same path length - they arrive in step whatever their wavelength, so the central image is white.

path difference of one wavelength

In certain directions to either side of the direct image, contributions arrive in step because the path difference from one gap is just one wavelength more than the path from its neighbour.

This experiment was safety-checked in February 2006