1. Interference Requirements
Need two (or more) wave
Must have same frequency and same polarizing direction
Must be coherent (i.e. waves must have definite phase relation)
Need two waves from single source taking two different path

2. Example

3. Example h

4. Example
Yellow light (wave length = 500 nm) illuminates a Mechelson’s interferometer. How many bright fringes will be counted as the mirror is moved through 1mm? d

5. Chapter 42 Diffraction

6. Interference Diffraction
When a light passes through a hole, or meets a disk etc., with dimensions comparable to the wavelength, we can see patterns on the screen behind them.
The wave nature of light*

7. Content of this Chapter
Diffraction and the wave theory of light
Single-slit diffraction
Intensity in single-slit diffraction
Diffraction at a circular aperture
Double-slit interference and diffraction
combined

8. Fraunhofer diffraction —infinite separation
Fresnel diffraction—finite separation

9. Huygens’ Principle:
All points on a wavefront can be considered as point sources for the production of spherical secondary wavelets. After a time t the new position of a wavefront is the surface tangent to these secondary wavelets.

10. The whole slit is divided into N strips so that the adjacent rays have path difference of a half-wavelength:

11. Width of the bright fringe at the center:
The other fringes:

12. Diffraction at a circular aperture
Single-slit diffraction
Diffraction at a circular aperture

13. Width of the bright fringe at the center:
Central maximum Dq
Diameter d
light

14. not resolved
resolved
just resolved
Two objects are just resolved when the maximum of one is at the minimum of the other.

15. Intensity in single-slit diffraction
The whole slit is divided into N strips with x = a/N, which can be regarded as Huygen’s wavelet, therefore,

16. Intensity in single-slit diffraction
The whole slit is divided into N strips with x = a/N, which can be regarded as Huygen’s wavelet, therefore,

20. Interference Diffraction
Two waves
Difference of Optical Path Length
Diffraction
One wave
Many waves

21. Interference

22. Interference
Diffraction

23. Interference Diffraction
Combined

24. Exercises
P , 9, 17, 27
Problems P

25. Interference Diffraction
Two waves
Difference of Optical Path Length
One wave
Many waves
Diffraction

26. Intensity in single-slit diffraction
Maximum at center
Minimum
Maximum

27. Width of the bright fringe at the center:
Central maximum q
Diameter d
light

28. Two objects are just resolved when the maximum of one is at the minimum of the other.
not resolved
resolved
just resolved

29. Double-slit Interference and Diffraction Combined
Each slit
Combined

30. Double-slit Interference and Diffraction Combined

31. The width of the central fringe is dependent on λ/a.
the first minimum
the mth maximum
missing fringes
if m=d/a

32. Example
A slit of width a = 0.5 mm is illuminated by a monochromic light. Behind the slit there placed a lens (f = 100 cm), and the first maximum fringe is observed at a distance of 1.5 mm from the central bright fringe on the focal plane (screen). Find the wavelength of the light, and the width of the central bright fringe.

33. Example
A typical astronomical telescope has a lens with a dimension of 10 m. Find the minimum resolving angle. Considering we use this telescope to observe the moon surface. What is the separation of two objects can just be resolved? (take wavelength of 540 nm)

34. Example
Two slits with separation of d = 5.5 mm is illuminated by a monochromic light. There are 21 fringes in the central maximum. What is the width of each slit?
The missing fringe is 11th.
a=d/11=0.5mm