Physics homework help.

Interference and Diffraction

Double Slit Theory:
The setup is that the two sources of coherent rays are separated by a distance d.  The screen where the waves are observed is so far away that the two rays are effectively parallel.
Use the space below to show that bright spots are found at angles defined by
.
Also show that bright spots will appear on a screen located a distance R away at locations defined by
 
Experiment
Equipment:

• Double and Single slits
• Diffraction grating
• Laser pointers (red, green, violet, blue, red-green)

 
 
 
Part 1: Double slit interference
Shine the green laser (λ = 532 nm) through the narrow double slit and project the pattern on a screen.
 
Be sure to keep both the slits and the screen perpendicular to the optical axis (light path). For best results, separate the screen and slits by the largest possible distance.
 
Double Slit Setup

Optical bench

 
 
 
 
 
 
 
 
 
Sketch and describe the observed pattern in the space below.  In your description, be sure to use the words “constructive”, “destructive”, “wavelength” and “pathlength difference”.
 
 
 
 
 
 
 
 
Measure the spacing between the central maximum and another maximum. For best results, make use of the symmetry, and measure to a large value of m.
 
Double slit green.jpg
Δy = _________         m_max/min= _______________   So your measured y_m is y_{_} =________
Measure the distance between the screen and the slit.
 
L = ______________________
 
Are you justified in using the small angle approximation? Y/N   Why?
 
 
 
Use the measured values and the nominal laser wavelength (on the body of the laser) to determine the slit spacing.
 
 
 
 
 
 
 
a= __________________
Part 2: Repeat Part 1 with the same slit, but a different colored laser (λ = 405 ± 10 nm). 
 
Double slit blue.jpg
What happened to the spacing of the pattern? Why?
 
 
 
Record your data. Clearly label your parameters.
 
 
 
Show your work to calculate the slit separation.
 
 
 
 
 
 
 
 
 
 
Do your answers from Part 1 and Part 2 agree to within a reasonable degree? Estimate some error to verify. Explain any assumptions.
 
 
Part 3: Attempt with the third laser pointer (λ = 655 ± 25 nm). Show your work if possible.
 
Double slit redgreen.jpg
 
Again, do your answers for the slit separation agree to within a reasonable degree with each other? With the nominal spacing on the slides?
 
 
 
 
 
For which data are you most confident? Why?
 
 
 
 
 
 
 
 
 
 
 
Part 4: Hair width
 
 
 
 
 
 
 
 
 
Remove the double slit completely and place a strand of hair in the path of the beam.
Why is a double slit pattern observed?
 
 
Measure the width of the hair.  Use the most appropriate laser for best precision.  Show your work.
Hair data cropped.jpg
 
 
 
 
 
 
Part 5: Single slit.
 
Theory
In this setup, the width is still much smaller than the distance to the screen, and the rays, all ∞ of them, are still parallel.  Use the space below to clearly show
 
 
 
 
 
 
 
 
 
 
Experiment:
Materials: Single slit, laser pointer, screen, mounts, ruler, meter stick
 
Choose a laser for precise results (remember your double slit experiments). Shine the laser light through the single slit and sketch the pattern in the space below.
 
Single slit A.jpg
 
Single slit B.jpg
Single slit C.jpg
 
 
Measure the width of the central fringe, 2y₁:___________________
What is the screen-slit distance, R? _____________        The laser wavelength λ? _______
Show your calculations to find the slit width a.
 
 
 
a=___________________________
 
How does it compare with the value indicated? Estimate the largest sources of error and decide whether your measured value is within a reasonable range of the nominal (listed) value of a.
 
 
 
Part 6: The diffraction grating.
 
Remove the single slit. Make sure your laser pointer is aimed at the wall, away from other groups. Add a transmission grating.  Be careful about stray beams – the small angle approximation is generally a very BAD approximation for diffraction gratings!
 
 
 
 
 
 
 
 
 
Diffraction Grating – Red Green setup
 
 
 
Diffraction grating redgreen data.jpg
 
How many orders do you see? That is, what’s the maximum value of m? _____
 
 
 
If you switch to another color of laser pointer, should you see more or fewer orders? Explain your prediction, below.
 
 
 
 
Now try it out. For extra clarity, mount both laser pointers simultaneously so they have a slight vertical offset, but the m=0 beams are lined up.
Diffraction Grating Green – right.jpg
 
Diffraction Grating Green – left.jpg
 
Was your prediction correct? (Y/N) If not, explain any misconceptions.
 
 
Let’s get quantitative. Turn off the laser pointer. Set up a CD in a three-fingered clamp such that it is nearly vertical. Aim the laser pointer at it, almost along the normal to the CD, so that the back reflections pass just over the laser pointer and hit the wall. You will want to maximize the CD-wall separation while not causing stray reflections to bounce all over the room. Sketch the geometry below, labeling all measured distances.
 
CD setup.jpg
 
 
 
 
 
 
 
 
 
 
 
Your diffraction pattern may not be perfectly symmetric.
CD A.jpg
 
CD B.jpg
 
 
 
 
Find the maximum value of m for which you can clearly observe both positive and negative diffraction spots. Measure the distance, then divide by 2 to account for small asymmetries.
m=______               Distance between order pairs: ________  Average y­_m=_________
 
What’s the CD-wall distance? ____________
 
Show your calculations to determine the groove spacing on a CD.
 
 
 
 
 
 
Distance between adjacent grooves: __________
 
Let’s do a check for reasonability. If the laser can resolve the distance between adjacent grooves, presumably it can also resolve the difference between pits of roughly the same spacing. Let’s calculate how much data we should be able to fit on the disk. Measure the active area of the disk. Sketch and record data below.
 
 
 
 
 
 
 
 
If we assume roughly square pits, how many such squares could you fit in the active area? Each pit is one “bit” of digital information. There are 8 bits in 1 byte. How many bytes can you fit on the disk? Show your calculation.
 
 
 
 
 
 
 
Experimental capacity: ________
 
Compare to the standard capacity of a CD. This may be listed on the disk, or you can search for a value and cite your source.
 
Accepted capacity: _____________            Source:
 
 
Discuss any discrepancies.
 
 
 
 
If time allows, repeat the experiment with a DVD-R. Show your data and calculations on extra paper as needed.
 
 
 
Explain the pros and cons of a Blu-Ray disk, using the information you have learned in this lab and about diffraction more generally.
 
 
 
 
 
 
 
 
 
 
Of the three experiments (double slit, single slit, and diffraction grating), which one came closest to the predicted values? Why do you think that is?

Physics homework help