Lab 12 Physics 2

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Lab 12: Interference and Diffraction Madeleine Mailloux, Raye-Julianne Delos-Reyes, Mariam Mostafa Goals : [A brief summary of the major experimental values to be obtained. Typically, a few sentences in length.] Part 1: Observe the basic characteristics of single slit diffraction by measuring λ, L, θ and a to find y. Part II: Cycle through the different slit patterns using the multi slit wheel, comparing maximum-to-maximum separation distance from the diffraction grating. Part III: Measure the wavelength of light using a diffraction grating. Procedure [A brief paragraph describing the apparatus used and measurements taken. Figures or images are helpful. Include modifications and revisions to the procedure if they are used.] Part 1: Arrange the laser, single slit wheel and screen on the optics bench according to the lab manual. Push the laser up against the diffraction slit wheel and place the screen about 30cm from the wheel. When in the 9 o’clock position, the slit aligns with the laser. Rotate the wh eel so the 0.08mm slit is aligned to the laser. Make the room as dark as possible in order to see the pattern on the screen. After a notable pattern is observed, slide the screen 70 cm from the slit. Rotate the slit disk wheel to cycle through all the slit widths (0.02 mm, 0.04 mm, 0.08 mm, and 0.16 mm). Observe and record how the width of the central maximum (equivalently 2x the distance to the first minimum) changes as a function of the slit width. Then, set the wheel to the 0.08 mm slit.

Next, the diffraction theory will be used to predict the width of the central maximum of our diffraction pattern. The single slit diffraction equation is 𝑠𝑖?𝜃 = ?𝜆 , where θ gives the angle at which the minimum of brightness occurs, pictured above. ‘ m ’ is the integer that indicates which minimum is being referenced, and λ is the wavelength of the light , where y is the distance along the screen, L is the distance between the slit and the screen, and a is the slit width. Using the fact that tan θ = y/L = sin θ (for small angles), we can substitute sin θ = y/L into the single slit diffraction equation, rearranging to express y in terms of λ, L, and a. Use this equation to predict y for the first minimum using known values of λ, L, and a. When measuring L, measure between the screen and the face of the slit wheel. The value for λ is found on the ba ck of the laser. Measure y directly by measuring the width of the central maximum using a ruler and then dividing it by 2. Then, find the percent difference between the predicted value and actual measured value. Then see if we can obtain a single slit diffraction pattern by making our own slit with two rulers or meter sticks. Part II: The single slit wheel should be removed and replaced with the multi slit wheel. The laser alignment should be adjusted until side patterns are displayed. Switch the multiple slit section of the wheel to increase the number of splits cycling through 2, 3, 4, and 5 slits observing each pattern. Make a prediction: How will the maximum-to-maximum separation distance for a grating compare to that of the double slit? Hint: the value of d for a grating is very, very small. Answer in question 5. d is the separation distance between neighboring slits. Remove the multi slit wheel and hold the diffraction gating in front of the laser. Adjusting of the screen may be needed to see first order maxima. Part III • Measure the distance along the screen y instead of the angle 𝜃 by using the definition of sine to substitute 𝑠𝑖?𝜃 = 𝑦 𝐿 into the diffraction equation. Rearrange to express 𝜆 in terms of y, L, and d.

• Set the screen to L = 10cm from the laser and hold the diffraction grating on the front of the laser. Use a meterstick to measure y, the distance from the center of the central maximum to the center of the first order maximum. • Find the wavelength 𝜆 of the laser light in units of nanometers by using the relation from step 1 and your values of y, L, and d. • Calculate the percentage error between the wavelength value calculated, and the actual wavelength of the laser printed on the back of the laser. • Turn off the laser. • Make a prediction on how the angle of diffraction for shorter wavelength violet light will compare to that of longer-wavelength red light. • Test the prediction by holding the diffraction grating up to your eye and looking at a white light source such as your phone’s flashlight. • Place the laser and single slit wheel back on the track. Use the two-dimensional pattern section of the wheel to produce diffraction patterns like those from DNA. Error and precautions: [Note at least one possible source of error, other than human error. Include how it could affect the results and suggest how one could avoid it. Error is the difference between true values and what we actually measure in the lab. Increasing precision reduces error, so any steps that you took (or could have taken) to increase precision can be described here. Repeating or replicating measurements helps determine whether there are errors and if they are random or systematic. If you only have time to take one measurement, you cannot determine how reproducible your results were, but you can still discuss what kinds of errors could be present. You may also choose to discuss assumptions that were made and how they affect the results.] Results: [This is the most important part of the report. Include the essential data in graphical or tabular format.] Part I: rewritten single slit diffraction equation in terms of λ, L, and a using small angle formula. Percent error. Questions: Question 1. How does the width of the central maximum change as you go to smaller and smaller slit width? Question 2. How is the double slit pattern different from that of the single slit? Are the locations of the minima of the single slit still present in the pattern of the double slit? Why do you think this is so? Question 3. How does the number of slits affect the sharpness or definition of the maxima in the multiple slit pattern? Are neighboring maxima more well-defined?

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Question 4. What are the two big differences between this double slit equation and the single slit equation? Question 5. Was your prediction correct? (It’s ok if not!) How did decreasing d by switching to the diffraction grating affect the separation distance and angle between neighboring maxima? Discussion: [Summary of conclusions drawn with references to values obtained. Include discussion of: 1) actual vs expected results, 2) fitting results, 3) reproducibility (confidence in results), 4) effects from sources of error if they significantly impacted results]

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