1. Unit 2 Particles and Waves Interference
CfE Higher Physics
Unit 2
Particles and Waves
Interference

2. Learning Intentions
Use correctly in context the terms: ‘in phase’, ‘out of phase’ and ‘coherent’, when applied to waves.
Explain the meaning of: ‘constructive interference’ and ‘destructive interference’ in terms of superposition of waves.
State that interference is the test for a wave.

3. Evidence of Waves and Particles
All waves can experience:
Diffraction
Refraction
Interference
The Doppler effect
All particles can experience:
The photoelectric effect

4. Constructive Interference
When two waves meet in phase (crest meets crest or trough meets trough) they combine constructively to produce a larger crest or trough. This is known as constructive interference. + =

5. Destructive Interference
When two waves meet completely out of phase (crest meets trough) they combine destructively to cancel each other out. This is known as destructive interference. + =

6. Coherent Sources
Two sources are coherent if they have the same frequency, velocity and have a constant phase relationship. They also tend to have the same amplitude.
Coherent sources can produce interference patterns of alternate areas of constructive and destructive interference. For example:
Two loudspeakers connected to the same source.
Light waves through a diffraction grating.
Interference is the test for a wave!

7. Learning Intentions

8. Path Difference and Interference
Interference from two coherent sources is due to the path difference (the distance each wave has travelled) between the waves:
n = 3 S1 S2 P
wave
source
double
slit
n = 2 ½
Alternate maxima and minima.
n = 2
n = 1 ½
n = 1
n = ½
n = 0
Central maximum
n = ½
n = 1
n = 1 ½
Pattern repeated either side.
Maximum (constructive interference).
n = 2
n = 2 ½
Minimum (destructive interference).
n = 3

9. Path Difference and Interference (continued)
At the central maximum the waves from the two slits have travelled the same distance and are therefore still in phase, so we get constructive interference.

10. Path Difference and Interference (continued)
For a maximum:
(whole number of wavelengths)
For a minimum:
(odd number of half wavelengths)

11. Worked Example
A pupil positions two loudspeakers connected to the same signal generator as shown below. As the pupil moves from the central maximum, at X, to point P four maxima are heard. Calculate the wavelength of the sound produced by the loudspeakers. X P A B
AP = 4.2 m
BP = 5.4 m

12. Learning Intentions
Describe the effect of a grating on a monochromatic light beam
Carry out calculations using the grating equation : dsinθ = nλ
Describe the principles of a method for measuring the wavelength of a monochromatic light source, using a grating

13. Diffraction Grating
A diffraction grating consists of many equally spaced slits that are extremely close together.
The width of each slit is so small that light is diffracted though each slit and interference takes place, as with the double slit.
A diffraction grating allows much more light to pass through and produces a clearer interference pattern.

14. Diffraction Grating (continued)
laser q
diffraction grating
screen
zero order maximum

15. Slits/lines per mm or m

16. Changes to the Experimental Set up

17. Changes to the Experimental Setup

18. Worked Example
A diffraction grating with 400 lines per mm is used to produce an interference pattern with light of a wavelength of 530 nm. Calculate the angle at which the 3rd order maximum is observed.
n = 3
530 nm
= 5.3 x 10-7 m 1
400000
d =
= 2.5 x 10-6 m ?

19. Learning Intentions
State approximate values for the wavelengths of red, green and blue light.
Describe and compare the white light spectra produced by a grating and a prism

20. Wavelength of Visible Light
Visible light consists of a range of wavelengths.
approximately: red nm
green nm
blue nm

21. Spectrum from a Prism only one spectrum
white light
Red
Orange
Yellow
Green
Blue
Indigo
Violet
only one spectrum
red light deviated least; violet most
bright
not very widely dispersed

22. Spectra from a Diffraction Grating
red
violet
white
white light
multiple spectra; symmetrical about central maximum
red light deviated most; violet least
not very bright
widely dispersed
central white image

23. Main Differences between a prism and grating for Spectra
The main differences in the spectra produced can be described as follows:
Prism
Grating
One Spectra produced
Multiple spectra on either side of the maxima – maxima is white.
Red deviated least, violet most
Violet deviated the least , red the most.
Spectrum produced by refraction
Spectra produced by diffraction and interference (higher order spectra are more spread out than the lower order spectra)