1. WAVE INTERFERENCE....

2. INTERFERENCE
Interference patterns are a direct result of superpositioning.
Antinodal and nodal lines are produced.
These patterns can be enhanced using diffraction gratings, where all waves pass through each other from multiple point sources.
We also learnt that the path difference for a point on a an antinodal line is always a factor of a wavelength, , whereas for a nodal line is half a wavelength, ½.
Antinodal line path difference = n
Nodal line path difference = n½
Where n = order 0, 1, 2, 3, …….

3. Birds eye view of 2 waves.... Red: crest meets crest
Or trough meets trough.
Constructive interference
Blue: crest meets a
trough and they cancel
out.
Destructive interference

4. Order of magnitude (m) Can be used to calculate the path difference.
Whole numbers: antinodal lines
Half numbers: nodal lines

5. Path Difference
6 wavelengths
5 wavelengths

6. S1 and S2 are two coherent sources
All points on a wavefront are in phase with one another S1 S2
Waves interfere constructively where wavefronts meet.
= antinodal lines 2
Wave Intensity
(Fringes) 1
n = order number
Along the nodal lines, destructive interference occurs.
Here antiphase wavefronts meet. 1 2
Nodal lines-out of phase by 180 deg, Antinodal lines in phase 360 deg.

7. A series of dark and bright fringes on the screen.
Young’s Double Slits
A series of dark and bright fringes on the screen.
Monochromatic light, wavelength l
Double
slit
Screen

8. Young’s Double Slit Experiment
THIS RELIES INITIALLY ON LIGHT DIFFRACTING THROUGH EACH SLIT.
Where the diffracted light overlaps, interference occurs
Double
slit
screen
Light
INTERFERENCE
Some fringes may be missing where there is a minimum in the diffraction pattern
Diffraction

9. Wave trains AP & BP have travelled the same distance
Assuming the sources are coherent
Wave trains AP & BP have travelled the same distance
(same number of l’s) A B P
Hence waves arrive
in-phase
CONSTRUCTIVE
INTERFERENCE
(Bright fringe)

10. Screen
Slits d L
d = slit separation
x = fringe separation

11. LASERS EMIT COHERENT LIGHT
Normal light sources emit photons at random, so they are not coherent.
LASER
LASERS EMIT COHERENT LIGHT

12. Example 5:
Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm.
Calculate the wavelength, , of the light used.

13. Example 5:
Monochromatic light from a point source illuminates two parallel, narrow slits. The centres of the slit openings are 0.80mm apart. An interference pattern forms on screen placed 2.0m away. The distance between two adjacent dark fringes is 1.2mm.
Calculate the wavelength, , of the light used.
SOLUTION:
The distance to the screen (2.0m) is large compared with the fringe spacing (1.2mm). The approximation formula can be used.
n = dx/L [n = 1 because the fringe spacing is being calculated]
= (8.0 x 10-4 x 1.2 x 10-3) / 2.0
= 4.8 x 10-7 m

14. WAVE INTERFERENCE....

15. Decide which points are Constructive interference and which are Destructive interference?

16. Interference
In phase
Out of phase
By 180 deg (half
a wavelength)

17. Youngs Double Slit Experiment
Quantum Physics.

18. Changing slit separation
Double slit animation.

19. A student uses a laser and a double-slit apparatus to project a two-point source light interference pattern onto a whiteboard located 5.87 meters away.
The distance measured between the central bright band and the fourth bright band is 8.21 cm. The slits are separated by a distance of mm. What would be the measured wavelength of light?
524 nm x10^-7

20. Changing slit separation.
As the separation decreases, the distance between lines increases.

21. Changing wavelength
As the wavelength increases, the spacing between nodal and antinodal lines increases

22. Path Difference
PD= m λ
Two point sources, 3.0 cm apart, are generating periodic waves in phase. A point on the third antinodal line of the wave pattern is 10 cm from one source and 8.0 cm from the other source. Determine the wavelength of the waves.
Two point sources are generating periodic waves in phase. The wavelength of the waves is 3.0 cm. A point on a nodal line is 25 cm from one source and 20.5 cm from the other source. Determine the nodal line number.
PD = 4.5cm, PD=mλ m=4.5/3 = 1.5.

23. The Diffraction Grating: This is a piece of glass with tiny slits made in it to produce small point sources.
A formula can be used to relate to the interference pattern produced by a particular diffraction grating.
dsin = n
(Where n = 0, 1, 2, 3 …….)
Often N, the number of slits per metre, or slits per centimetre is given. The slit spacing d is related to N by:
d = 1/N

24.  AC = AB sin  and AB is the grating element = d Hence d sin  = n
For light diffracted from adjacent slits to add constructively, the path difference = AC must be a whole number of wavelengths.
Grating A C
Monochromatic light  B
AC = AB sin  and AB is the grating element = d
Hence d sin  = n
d = grating element

25. DIFFRACTION GRATING WITH WHITE LIGHT
Hence in any order red light will be more diffracted than blue.
A spectrum will result
Several spectra will be seen, the number depending upon the value of d
Second Order maximum, n = 2
Grating
First Order maximum, n = 1
White Central maximum, n = 0
First Order maximum, n = 1
Second Order maximum, n = 2
screen

26. Note that higher orders, as with 2 and 3 here, can overlap
Note that in the spectrum produced by a prism, it is the blue light which is most deviated
grating

27. Calculate the wavelength of the light.
Example: Light from a laser passes through a diffraction grating of 2000 lines per cm. The diagram below shows the measurement made.
laser
0 order 
0.5m
Grating 2m
2nd order
Calculate the wavelength of the light.
SOLUTION:
Slit spacing d = 1/N
= 1/200000
= 5.00 x 10-6m
sin = 0.5/2
= 0.250
= 6.25 x 10-7m
 = dsin/n
= (5.00 x 10-6 x 0.250) / 2

28. http://webphysics. ph. msstate