1. The Geometry of Interference and Diffraction
SPH4U

2. Two Point Source Interference
Consider the interference pattern for two point sources in phase (e.g., two slits).
nodal line
constructive interference

3. In Phase
Along the line halfway between the two slits, the waves will be in phase because the path length is the same. A bright spot would appear on the screen.

4. In Phase
Along the line halfway between the two slits, the waves will be in phase because the path length is the same. A bright spot would appear on the screen.
This bright spot is called the central maximum.

5. Out of Phase
A little to the side of the central maximum (at an angle q), the path difference between the waves is ½l, and the waves will arrive out of phase, creating a dark spot.

6. In Phase
A little bit further to the side and the path difference is l. The waves will be in phase again, creating another bright spot.

7. The Dark Spots
Let’s find the position of each of the dark spots, where the path difference is (n – ½)l.

8. The Dark Spots
n = # of dark spots from the central maximum d = separation between slits L = distance to the screen xn = distance between dark spot and central maximum

9. The Dark Spots

10. The Dark Spots

11. The Dark Spots

12. Example
Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

13. Example
Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

14. Example
Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

15. Example
Light from a monochromatic source is directed through two slits separated by 0.22 mm and an interference pattern is created on a screen 3.0 m away. If the separation between the first and seventh nodal lines is 5.0 cm, what is the wavelength of the light?

16. The Bright Spots
Similarly, for bright spots away from the central maximum:

17. Diffraction Gratings
A diffraction grating has a large number of equally spaced slits and a similar interference pattern.
The primary difference between the patterns is that the maxima are much brighter and sharper.

18. Diffraction Gratings
The locations of the maxima are still given by

19. Single Slit Diffraction
Diffraction through a single slit may be analyzed similarly.

20. Huygen’s Principle
Consider each of the points along the slit as a point source of wavelets. The wavelets will all be in phase at the central maximum.

21. Out of Phase
At some angle q, there is a l path difference between the top and bottom of the slit.
Each point therefore has a l/2 (out of phase) partner: 1 and 7, 2 and 8, etc., resulting in destructive interference.

22. Out of Phase
At some angle q, there is a l path difference between the top and bottom of the slit.
Each point therefore has a l/2 (out of phase) partner: 1 and 7, 2 and 8, etc., resulting in destructive interference.
y just to help differentiate the equations

23. Similarly
Secondary maximum Second dark spot

24. Minima
The minima occur at

25. Example
Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

26. Example
Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

27. Example
Monochromatic light of wavelength 670 nm passes through a slit width of 12 mm. A screen is placed 0.30 m away. What is the width of the central maximum?

28. Resolution
Resolution is the ability of an instrument to separate the images of two objects.

29. Resolution
The smaller the aperture, the greater the diffraction and the lower the resolution.

30. More Practice Textbook Questions p. 473 #2, 5, 6 p. 504 #2, 4, 5
Tomorrow:
Interference of Light Lab