Key areas Conditions for constructive and destructive interference

Key areas • Conditions for constructive and destructive interference. • Constructive and destructive interference in terms of phase between two waves. • Coherent waves have a constant phase relationship and have the same frequency, wavelength and velocity. • Interference of waves using two coherent sources.

What we will do today: • Revise some basic wave definitions. • Use correctly the terms “in phase”, “out of phase” and “coherent” when applied to waves. • Explain the meaning of “constructive interference” and “destructive interference”. • State that interference is a test for a wave. • State that reflection, refraction, diffraction and interference are characteristic behaviours of all types of waves.

Waves Revision

Wave Characteristics • Period = 1 / frequency • Period, T: the time taken for one complete wave to pass a point (s). • Frequency = 1 / period • Frequency, f: the number of waves per second (Hz)

• The frequency of a wave is the same as the frequency of its source. • (Provided the source doesn’t move).

• The energy of a wave depends on its amplitude (a). a

2007

Wave Equation • Wavelength, λ: the length of one wave (m). • Frequency, f: the number of waves per second (Hz). • Wave speed, v: the speed of a wave (ms-1) • They are all related by the equation: v=fλ

Interference and Path Difference

Phase • Two waves in phase. • Maximum and minimum points on the wave occur at the same time.

• Two waves completely out of phase. • The maximum of one wave occurs at the minimum of the other and vice versa.

Coherent Sources • If waves coming from two sources have the same frequency, wavelength and velocity and are in phase, then the two sources are coherent. • They will also have the same amplitude. • Coherent light is light which has no phase difference.

Cf. E Specimen Paper

Wave Characteristics • Reflection, refraction, diffraction and interference are characteristic behaviours of all types of waves. • We have previously covered the first three.

1. Reflection • • • Waves reflect off a surface. The angle of incidence (incoming angle) is equal to the angle of reflection (outgoing angle). i=r

2. Refraction • Waves change speed usually with a change in direction when passing from one medium to another (eg air to water).

3. Diffraction • • • Waves ‘spread out’ round corners. When passing through a gap the waves appear to curve. If the gap is similar to the wavelength then circular wavefronts are produced.

Interference • When two sets of waves meet, they combine to produce a new pattern. • The new pattern depends on the original wavelengths, amplitudes etc. • Waves combine in one of two ways: a. Constructive Interference. b. Destructive Interference l Interference is the test for a wave.

2012 Revised

Answer • Refer to previous lesson on light travelling as particle in photons. • Discuss how light produces interference so also acts as a wave. • Conclusion – light is both

Constructive Interference Two sets of waves meet in phase. Two crests meet or two troughs meet to produce a larger crest or trough. + =

Destructive Interference + =

Two sets of waves meet completely out of phase (i. e. 180º out of phase). A crest meets a trough and combine to cancel each other out and produce no wave at that point. Note that if waves are not of equal amplitude, then complete cancelling does not occur.

Path Difference An interference pattern is more easily explained in terms of path difference. Consider an interference pattern produced by two coherent wave sources as shown below.

A C B Wave Source Double Slit The two wave trains travel equal distances (AC = BC). i. e. There is no path difference. Screen

C A B Wave Source Double Slit Path Difference The two wave trains travel different distances. There is a path difference. Screen