Lab Report #10

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manualInterferenceandDiffractionofLight1.docx

temple university physics

Interference & Diffraction of Light

Diffraction refers to the ‘bending’ of waves when they strike barriers with sharp edges or pass through small apertures. After diffracting, the light waves from different points mix causing regions of constructive and destructive interference, or lighter and darker regions, respectively. Diffraction can seem abstract, but it can be visualized using Huygens’ principle, which simply states that every point on a wavefront acts like its own source of waves. Each of these individual sources sends waves radially outward, so the light from different points cross paths and interfere with each other.

Note that modeling light as a ray or a particle does not predict this interference and diffraction because rays and particles would just travel straight through the apertures without bending or interfering.

Let’s do a quick demonstration to get us started. It’s easy to see diffraction firsthand if you have a bright LED like that on most smartphones. Go to a dark room with a flat wall. Turn on the LED and hold it about a foot from the wall to illuminate the wall in front of you. With your other hand, place a finger near the LED to block about half the light and cast a shadow on the wall. Look for a concentric dark line outlining the shadow of your finger, if you don’t see the line, move your finger nearer or farther from the LED while looking for the line. If you look closely there is actually a series of light and dark lines, this is due to light diffracting around the edge of your finger and interfering with itself constructively to form bright lines, and destructively to form dark lines. This same effect can be seen on the shadows of buildings on a sunny day.

Learning goals for this laboratory:

· Understand how diffraction patterns form

· Be able to distinguish between single and multiple slit patterns

· Understand what properties of the slit affect the pattern

· Know how to calculate the wavelength of the light using the pattern

· Understand how diffraction is used to obtain molecular structure

Part I. Single slit diffraction

Watch this video which shows several interference and diffraction phenomena:

https://www.youtube.com/watch?v=9D8cPrEAGyc

1. Refer to the single slit diffraction part of the video, which runs from the beginning to the 1:05 mark. Single slit diffraction is shown using a red laser. A closeup view is shown starting at the 40 second mark. Notice that the laser light is spread out into a series of bright spots, or maxima, by passing it through a single slit. The width of the central maximum is greatest.

2. For the data section of your report, record your visual observations on how the width of the central maximum and the spacing between adjacent maxima changes as the slit width is increased and decreased. Note that only the slit width is changed here, there is no camera zooming or anything else causing this pattern to change. See the figure on the next page defining what is meant by maxima and minima.

Image credit: Nora Dean

Question 1. What happens to the width of the central maximum as the slit width increases? Is your observation consistent with the single slit diffraction equation? Support your answer using mathematical reasoning. If necessary, refer to your text to obtain the single slit diffraction equation.

Question 2. What would be different about the single slit pattern if we used a different wavelength of light, say green, rather than red? Use the single slit diffraction equation to support your answer.

Part II. Pinhole diffraction

This part of the demonstration shows light shining through a small circular aperture, a pinhole.

1. Continue watching the video through the part showing pinhole diffraction (up to the 1:40 mark).

2. For the data section of your report, record your observations on the similarities and differences between the single slit pattern from Part I and the pinhole pattern.

Question 3. When viewing objects through a telescope or microscope, the light must pass through a lens that acts just like a pinhole above. Consider observing two stars that are very close together through a telescope. How does diffraction limit the telescope’s ability to resolve the stars as two separate points of light?

Question 4. In order to better resolve two neighboring molecules using a microscope, would it be better to use a shorter or longer wavelength of light? Explain your reasoning using what we know about the relationship between the angle of spread and the wavelength of light according to the single slit diffraction equation.

Part III. Double slit diffraction

1. Watch the double slit diffraction part of the video. You will see double slit diffraction for three different wavelength lasers. Pause the video at the 2:22 mark to where all three patterns are clearly shown.

2. Compare the pattern made by red light on a single slit at the 1:03 mark to the pattern made by red light on a double slit at the 2:22 mark. For the data section of your report, record your observations on the similarities and differences between the single slit and double slit patterns for red light. Note that in double slit patterns the smaller segments within the overall envelope are referred to as fringes.

3. Next, let’s use the double slit patterns to measure the wavelength of the light. Go to the 2:22 mark in the video and use a ruler to measure the distance between the central line and the 1st order maximum. See example below. If you don’t have a ruler, you can download the Physics Toolbox Suite app for your phone, which has a ruler. Measure the distances to the nearest 1/100th of a cm. Record your results for all three colors of light.

4. Let’s do some math to use the distance measurement between the central line and first order maximum in our double slit equation.

First, for small angles of like in our experiment we can use the approximation .

Second, we can substitute out the angle for the distance using the arc length equation where is the distance between the double slit and the screen, and is the distance on the screen you measured above.

Combining these into our double slit equation we get

Noting that = 1 for the 1st order maximum.

5. Use the equation to determine the wavelength of the green laser and orange laser assuming the red laser is a helium-neon laser which has a wavelength of 632.8 nm.

Question 5. In spectroscopy, an unknown element can be identified by the characteristic wavelengths of light that it emits. How could one use the double slit pattern to determine the wavelength of the light emitted by a sample? Use the double slit interference equation to support your answer. Assume the experimenter has control over the slit spacing and can measure the angle of diffraction.

Question 6. Knowing that the condition for destructive interference is met at more values of as more and more slits are added, would you expect the number of fringes to increase or decrease as you increase the number of slits? Support your answer with physical reasoning.

Part IV. Diffraction in crystals

A diffraction grating is a lot of narrow slits closely packed together. The equation used for diffraction gratings is the same as that for double slits. Let’s see how the patterns look for diffraction gratings in comparison to single and double slit patterns.

1. Click “Play” on the simulation here (it can play directly in the web browser)

https://phet.colorado.edu/en/simulation/wave-interference

2. Double-click on the Diffraction option. Turn on the laser by clicking the red button and you should see a pattern for a pinhole. This is an idealized version of the pattern we saw in the video in Part II.

3. Toggle back and forth between this single hole and the grid array of holes (the fourth option down) and observe how the pattern changes for more holes.

4. For the data section of your report, record your observations on the similarities and differences between the single hole pattern and the multiple hole pattern.

Question 7. When going from a single slit to a double slit, we saw fringes appear in the diffraction pattern. What happens to the appearance of the pattern in the analogous 2-D situation when you go from a single hole to multiple holes?

5. C:\Documents and Settings\tue77829\My Documents\labs\images\Lab 39 images\Rosalind_Franklin_Plate_1_DNA_B_form_1000.jpgWe saw how diffraction is useful for measuring the wavelength of light. Diffraction is also extremely useful for mapping the structure of biomolecules. This is how double-helix structure of DNA was discovered by Rosalind Franklin in 1953, a picture of the original photo is shown at right. This pattern was made by crystallizing a large number of identical DNA molecules into a regular array (a crystal) then shining x-rays through the crystal.

Question 8. Explain mathematically using the diffraction equation why one must use x-rays to see a pattern when diffracting through a crystal of DNA. (Note that the wavelength of x-rays is 0.1 nm.)

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7/23/2020 2:03 PM