1. Interference Introduction to Optics Coherent source
Two Slit Interference
Thin film interference
Interference from a Grating

2. Interference
Waves
Mechanical
Electromagnetic
Matter

3. Interference
Optics
Geometric Optics
Physical Optics

4. Interference Coherence and Monochromatic
No coherence between two light bulbs
coherence - two or more waves that maintain a constant phase relation.
Coherence time
Coherence length
Some later time or distance
monochromatic - a wave that is composed of a single frequency. Heisenberg uncertainty relation.

5. Huygens’ Principle
Every point on a wave is its own wave source

6. Interference Single Slit Interference
We use Huygens’ Principle to understand why a single slit opening would yield and interference pattern.

7. Interference Double Slit Interference
With two slits, constructive interference occurs with the path lengths from both slits are the same. Destructive interference occurs when the path lengths are out of phase.
PHET ripple tank +1 -1

8. Difference Between Single Slit and Double Slit

9. Comparing Single Slit and Double Slit
-m represents dark spots
-Larger central maxima
-width can be analogous to half the distance between slits
DOUBLE SLIT:
-m represents bright spots
-more fringes (due to the separation analogy)

10. Interference

11. Interference

12. Interference Double Slit Interference
Write the equation that allows you to calculate the position of the bright fringes as a function of angle.
Write the equation that allows you to calculate the position of the bright fringes as a function of displacement ym from the center line.
The labels we used to label the bright spots is called the order m.

13. Interference
Ideal
Real

14. Class Question
Suppose the viewing screen in the figure is moved closer to the double slit. What happens to the interference fringes?
1. They get brighter but otherwise do not change.
2. They get brighter and closer together.
3. They get brighter and farther apart.
4. They get out of focus.
5. They fade out and disappear.

15. Class Question
Suppose the viewing screen in the figure is moved closer to the double slit. What happens to the interference fringes?
1. They get brighter but otherwise do not change.
2. They get brighter and closer together.
3. They get brighter and farther apart.
4. They get out of focus.
5. They fade out and disappear.

16. Class Question
Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. How large is l2 relative to l1?
1. l2 is larger than l1.
2. l2 is smaller than l1.
3. Cannot be determined from this information.

17. Class Question
Light of wavelength l1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to l2, the fringes get closer together. How large is l2 relative to l1?
1. l2 is larger than l1.
2. l2 is smaller than l1.
3. Cannot be determined from this information.

18. Interference Multi-slit Interference
Next we would like to see what happens if we increase the number of slits from 2 to 3, 4, 5, etc. We will setup a slide (1 inch X 5 inches) with different slit patterns. The numbers across the top indicate the number of slits. Thus 4 indicates four slits. We will use the same set-up as before and observe the slit pattern for the double and triple slits. Do you see any difference between the two patterns? Discuss this and write your answer.

19. Interference
Observe the pattern for 4 and 5 slits. Do you see any pattern developing between the number of slits and the interference pattern? Explain.

20. Interference Diffraction Grating What is a diffraction grating?
What are the two types?
A diffraction grating is a slide with a large number of slits. Usually expressed in the number of slits per mm.
transmission and reflection gratings

21. Interference
We have set up a transmission diffraction grating with a laser and a white light source. Observe the spectra from a white light source and laser. Can you see more than first order from the grating and laser? Can you see more than one spectra from the white light source? Discuss what you each see in your group. Draw the light pattern from the laser and white light source below.
laser
white
light

22. Interference
You should see at least two spectra, one to the right and one to the left. If you look real far the the right and left you will see two more. The different spectra are the different orders. and compare the figure with what you see.

23. Interference

24. Class Question
White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow,
1. the red side is on the right, the violet side on the left.
2. the red side is on the left, the violet side on the right.
3. the red side is closest to the center of the screen, the violet side is farthest from the center.
4. the red side is farthest from the center of the screen, the violet side is closest to the center.

25. Class Question
White light passes through a diffraction grating and forms rainbow patterns on a screen behind the grating. For each rainbow,
1. the red side is on the right, the violet side on the left.
2. the red side is on the left, the violet side on the right.
3. the red side is closest to the center of the screen, the violet side is farthest from the center.
4. the red side is farthest from the center of the screen, the violet side is closest to the center.

26. Interference Thin Film Interference
The most common example of interference is interference in thin films. One example of this is an oil slick. This is a thin film of oil on top of water. You find this a lot of times on a road after a rain storm. You will see bands of different colors on the surface of a puddle. The different colors come from the varying thickness of the oil film. Can you explain this?

27. Interference
We can also use interference to measure the thickness of small objects as shown in the following example. For interference from a thin film we need to consider two things:
1. The phase shift when the light (wave) is reflected at both surfaces.
2. The phase shift do to the difference in length of the two paths.

28. Interference
First lets consider the phase shift do to the reflection from an interface between two different materials with different indexes of refraction. What happens when light is reflected from a interface with the second medium having a larger index? We can use the analogy of a wave on a string being reflected from a fixed end. Do you recall what happen to the reflected pulse? Draw the reflected pulse on the top diagram below.

29. Interference
Does the light wave come back in phase or out of phase? Discuss this in your group.
string
fixed end
light
medium with
smaller index
180 degree or l/2 phase shift on reflection

30. Interference
Do the same for light reflected from a medium with a smaller index of refraction. Draw the reflected light wave on the lower diagram. This is like a wave on a string being reflected from a free end.
string
free end
light
medium with
larger index
0 degree phase shift on reflection

31. Interference
Does the light wave come back in phase or out of phase? Discuss this in your group.
l/2 phase shift
no phase shift

32. Interference Lets do an example. Light is reflected from an oil slick:
a thin film of oil on top of water.
incident beam
reflected beam
air
oil
water