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

Interference Waves Mechanical Electromagnetic Matter

Interference Optics Geometric Optics Physical Optics

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.

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

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

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

Difference Between Single Slit and Double Slit

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)

Interference

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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.

Interference Ideal Real

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 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 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 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.

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.

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.

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

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

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.

Interference

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 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.

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?

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.

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 l/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. l/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. incident beam reflected beam air oil water