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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 experiment 2. Galileo’s observation of Jupiter’s moons

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interference

Interference

Introduction to Optics

Coherent source

Two Slit Interference

Thin film interference

Interference from a Grating

reading question
Reading Question

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

1. Young’s double slit experiment

2. Galileo’s observation of Jupiter’s moons

3. The Michelson-Morley interferometer

4. The Pound-Rebka experiment

5. Millikan’s oil drop experiment

reading question1
Reading Question

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

1. Young’s double slit experiment

2. Galileo’s observation of Jupiter’s moons

3. The Michelson-Morley interferometer

4. The Pound-Rebka experiment

5. Millikan’s oil drop experiment

reading question2
Reading Question

What is a diffraction grating?

1. A device used to grate cheese and other materials

2. A musical instrument used to direct sound

3. A plaque with a tiny circular aperture

4. An opaque objects with many closely spaced slits

5. Diffraction gratings are not covered in Chapter 22.

reading question3
Reading Question

What is a diffraction grating?

1. A device used to grate cheese and other materials

2. A musical instrument used to direct sound

3. A plaque with a tiny circular aperture

4. An opaque objects with many closely spaced slits

5. Diffraction gratings are not covered in Chapter 22.

reading question4
Reading Question

When 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 question5
Reading Question

When 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.

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Interference

Waves

Mechanical

Electromagnetic

Matter

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Interference

Optics

Geometric Optics

Physical Optics

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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.

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

Interference

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.
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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

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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.
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Bright spot

m = 0, 1, 2, 3 …

Interference

Double-Slit Interference (Young’s Experiment)

ym

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Interference

Double Slit Interference

  • Can you explain what the two patterns look like for a red and green laser?

+1

0

-1

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Interference

Ideal

Real

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Interference

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 mm

L = 8 m

ym+1 - ym = 910 mm

class question
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.

class question1
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.

class question2
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.

class question3
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.

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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?
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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.

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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.
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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

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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

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Interference
  • Does the light wave come back in phase or out of phase? Discuss this in your group.

no phase shift

l/2 phase shift

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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

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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.
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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

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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.
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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

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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

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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. Look at Figure 37-23 (page 971) and compare the figure with what you see.
class question4
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.

class question5
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.