1. Wave superposition
If two waves are in the same place at the same time they superpose.
This means that their amplitudes add together vectorially
Positively when they are in phase

2. Wave superposition
If two waves are in the same place at the same time they superpose.
This means that their amplitudes add together vectorially
Negatively when they are in antiphase

3. The conditions for two waves to interfere with each other
The waves must be coherent.
This means there must be a constant phase difference between them ( which also implies that they have to be of the same frequency.)
Interference between water waves from coherent sources

4. Interference Is best understood with relatively long waves
Interference Is best understood with relatively long waves. Both water waves or microwaves (3cm ) provide a reasonable model. Coherence of the waves is ensured by obtaining the waves from a single frequency microwave source ( a monochromatic source)
The waves are passed through two slits and are diffracted in the process. (That is they begin to spread out as if the slit was at the centre of a circular wave front)
On a wave front diagram the waves positively superpose where they cross and negatively superpose in the centre of the gaps.

5. A microwave detector moved normal to the source detects positive and negative superposition called interference fringes.

6. Each peak is produced by positive interference
Each peak is produced by positive interference. Each trough occurs because of negative interference

7. Central maximum phase difference 0
Here the path lengths from S1 and S2 to X are the same

8. path difference to next peak is 1 wavelength
2 wavelenghts S1
3 wavelengths S2
Note that when the phase difference is 2π the path length from one of the slits is longer by a single wavelength

9. Path difference 2 wavelengths

10. Measuring the difference in path length to the first fringe
Zero or central fringe
0.670m
In this case λ= = 0.025m.

11. Interference with Light Sources
The geometry of the situation gives us the relationship
W is the distance between adjacent fringes
S is the slit separation D
laser
double slit
The laser is a coherent light source which is divided into two by the fine double slit The screen is at a distance of 5-10m. The interference pattern below is produced. The fringes are equally spaced.

12. In reality you would measure the total distance between the centre of several visible fringes and divide by the number of dark intervals between them to achieve a better value for w.

13. Diffraction of Waves

14. Diffraction from a Single Slit
Through a narrow single slit the wave front spreads out. If the slit is wide the spreading is slight. If the slit is comparable in width with the wavelength of the wave the spreading is large.

15. Diffraction of water waves from above

16. Single narrow slit
Laser

17. The diffraction of light
Diffracted laser light from a single slit projected onto a screen
Notice there is a large central maximum with minima and secondary maxima on each side of it.
The diffraction pattern can be explained by assuming that each point along the slit width is a wave source:
Superposition then accounts for the bright and dark areas in the pattern.

18. intensity 2nd order Principle maximum 1st order Principle maximum
Zero order principle maximum
1st order
Principle maximum
2nd order
Principle maximum
minimum
minimum
minimum
minimum

19. Imagine one set of rays produced normal to the slit.
Normal rays
Slit width a
The path length of this set of rays to the screen are all equal. The waves reinforce each other and produce a bright region on the screen

20. How the minima are produced
A second set of ray can emerge from the slit all parallel to each other but at an angle θ to the normal rays. . θ
a/2n a
a/2n
a/2n
a/2n
These rays can be equal distances apart. We can think of the slit being divided into d/2n equal strips

21. Difference in path length between ray A and ray B
These rays will have a difference in path length to the screen θ A
Difference in path length between ray A and ray B B

22. Difference in path length
When the path difference =λ/2 they will interfere destructively with each other θ A
Difference in path length
λ/2 B

23. Difference in path length
The same is true for every pair of rays parallel to rays A and B for example rays C and D and so on. θ A
Difference in path length B
λ/2 C D
Because these waves destroy each other no light appears along these directions.

24. Difference in path lengthX
λ/2 θ θ Y
Difference in path length
And minima occur when n=1,n=2,n=3 etc

25. The diffraction grating
A typical diffraction grating is an arrangement of identically spaced diffracting elements. Normally a large number of parallel lines are ruled on glass. The diffracting elements are the gaps between the ruled lines. typically there would be around 600 lines per mm.

26. Each line acts as a very narrow slitB θ θ C
The light through each slit is diffracted in all directions.
Consider the light through two slits diffracted at angle θ to the normal
If the light diffracted through angle θ at A is in phase with the light diffracted through θ at B it must be in phase with the light at this angle through every other slit.

27. The path difference is the length ANθ A X N d θ Y
Notice that:
to be in phase
the path difference (ie the distance A to N)
has to be a multiple of the wavelength λ
i.e (n λ )
The distance AN = d sinθ
So d sinθ = n λ

28. What you see
When the waves interfere constructively through each slit they are at an angle given by the formula
d sinθ = n λ

29. Question
When a grating of 300 lines per millimetre is illuminated with parallel beam of monochromatic light normal to it a second order principle maximum is observed at to the straight through direction. Calculate the wavelength of the light.