Interference

Introduction to Optics

Coherent source

Two Slit Interference

Thin film interference

Interference from a Grating

Reading Question

What was the first experiment to show that light is a wave?

1. Young’s double slit experiment2. Galileo’s observation of Jupiter’s moons3. The Michelson-Morley interferometer4. The Pound-Rebka experiment5. Millikan’s oil drop experiment

Reading Question

What was the first experiment to show that light is a wave?

1. Young’s double slit experiment2. Galileo’s observation of Jupiter’s moons3. The Michelson-Morley interferometer4. The Pound-Rebka experiment5. Millikan’s oil drop experiment

Reading QuestionWhat is a diffraction grating?

1. A device used to grate cheese and other materials2. A musical instrument used to direct sound3. A plaque with a tiny circular aperture4. An opaque objects with many closely spaced slits5. Diffraction gratings are not covered in Chapter 22.

Reading QuestionWhat is a diffraction grating?

1. A device used to grate cheese and other materials2. A musical instrument used to direct sound3. A plaque with a tiny circular aperture4. An opaque objects with many closely spaced slits5. Diffraction gratings are not covered in Chapter 22.

Reading QuestionWhen laser light shines on a screen after passing through two closely spaced slits, you see

1. a diffraction pattern.2. interference fringes.3. two dim, closely spaced points of light.4. constructive interference.

Reading QuestionWhen laser light shines on a screen after passing through two closely spaced slits, you see

1. a diffraction pattern.2. interference fringes.3. two dim, closely spaced points of light.4. constructive interference.

Interference

Waves

Mechanical MatterElectromagnetic

Interference

Optics

Geometric Optics Physical Optics

a a

InterferenceCoherence and Monochromatic No coherence between two light bulbs

Coherence timeCoherence length

Some later time or distance

coherence - two or more waves that maintain a constant phase relation.

monochromatic - a wave that is composed of a single frequency. Heisenberg uncertainty relation.

Double Slit Interference We will work through this tutorial together. We have setup a

laser and a slide (2 inches X 2 inches) with different double slit patterns labeled A, B, and C. First we will look at double slit A. On the wall you will see a double slit interference pattern. Draw the interference pattern below and mark the center bright spot. Label the center bright spot 0. Label the next bright spot on the right +1. Continue to label the spots +2, +3, etc. Do the same for the spots on the left but label them -1, -2, -3, etc.

-3 -2 -1 0 +1 +2 +3

Interference

Double Slit Interference Below we have reproduced Figure 37.5 on page 975. On the

figure label the points that corresponds to the orders -2, -1, 0, +1, and +2. If the lines represent a crest then where two crest cross is a bright spot.

+1

0

-1

Interference

Interference

Interference

sbrightspot3,2,1,0sin mmd

This is a little misleading

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.

sbrightspot3,2,1,0sin mmd darkspots3,2,1,0

21

sin

mmd

sbrightspot3,2,1,0 md

Lmym

Interference

Double-Slit Interference (Young’s Experiment)

mdL

ym

Interference

ym

Bright spot

d sin mm = 0, 1, 2, 3 … md tan

mLy

d m

Double Slit Interference Can you explain what the two patterns look like for a

red and green laser?

+1

0

-1

Interference

InterferenceIdeal Real

Double-Slit Interference (Young’s Experiment) Measure the distance from the slits to the screen and calculate

the wavelength for the laser. The separation between the slits is 0.6 mm.

d = 0.6 mmL = 8 m

ym+1 - ym = 910 mm

d sin m mdL

ym

Interference

mm yy 1

11 mdL

ym

mdL

mdL

1 dL

mmdL 1

Lyyd mm 1 nm

m

mmmm700

8

106.0

Student Workbook

Student Workbook

Student Workbook

Student Workbook

Class QuestionSuppose 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.

Class QuestionSuppose 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.

Class QuestionLight of wavelength 1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to 2, the fringes get closer together. How large is 2 relative to 1?

1. 2 is larger than 1.2. 2 is smaller than 1.3. Cannot be determined from this information.

Class QuestionLight of wavelength 1 illuminates a double slit, and interference fringes are observed on a screen behind the slits. When the wavelength is changed to 2, the fringes get closer together. How large is 2 relative to 1?

1. 2 is larger than 1.2. 2 is smaller than 1.3. Cannot be determined from this information.

InterferenceThin 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?

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.

Interference

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.

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 /2 phase shift on reflection

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

Interference Does the light wave come back in phase or out of phase?

Discuss this in your group.

/2 phase shift no phase shift

Interference Lets do an example. Light is reflected from an oil slick:

a thin film of oil on top of water.

air

oil

water

incident beam reflected beam

InterferenceMulti-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.

Interference

Draw the triple slit interference pattern below.

-3 -2 -1 0 1 2 3

Draw the interference pattern for 4 slits.

-3 -2 -1 0 1 2 3

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.

InterferenceDiffraction 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

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.

whitelight

laser

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. Look at Figure 37-23 (page 971) and compare the figure with what you see.

Interference

Interference

,3 ,2 1, 0,

sin

m

md m

Student Workbook

Student Workbook

Student Workbook

Student Workbook

Class QuestionWhite 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.

Class QuestionWhite 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.

Class Question