Activity 1: Diffraction of Light

Transcription

1 Activity 1: Diffraction of Light When laser light passes through a small slit, it forms a diffraction pattern of bright and dark fringes (as shown below). The central bright fringe is wider than the others. The angle ( ) between the center of the middle bright fringe and the center of the first dark fringe is related to the width (W) of the slit and the wavelength ( ) of the light by sin W. NOT TO SCALE L y Pattern Experiment W First, you will use the diffraction pattern produced by a laser shining through a slit to determine the laser s wavelength. 1. Set up the red laser to pass through a single narrow slit and a diffraction pattern appears on the screen. The screen should be about 1 meter from the slit. Record the width of the slit used below. 2. Tape a piece of paper to the screen and sketch the pattern that appears on the screen. Mark the middle of the pattern. Slit 3. How does the width of the central bright fringe compare to the widths of the other bright fringes? 4. Measure the distance between the slit and the screen. 5. Determine the distance (y) between the middle of the central bright fringe and the middle of the first dark fringe on one side of the pattern (as shown in the diagram above). It is easier to measure the distance between the centers for the dark fringes on either side of the central bright fringe and divide that distance by two.

2 6. Using trigonometry, calculate the angle to the middle of the first dark fringe. (Hint: Sketch what you measured.) 7. Using the width of the slit (W), calculate the wavelength of the laser. Show all of your work. 8. How does your measurement compare to the known wavelength of the red laser (650 nm, 1 nm = 10-9 m)? Calculate the percent difference. 9. Qualitatively, how do you expect the single-slit diffraction pattern to change if slit were narrower? Assume everything else about the setup remains the same. Explain your reasoning. 10. Qualitatively, how do you expect the single-slit diffraction pattern to change if a green laser ( = 540 nm) is used instead of a red laser? Assume everything else about the setup remains the same. Explain your reasoning. Second, you will use a diffraction pattern to determine the width of a hair. Surprisingly, a narrow barrier will produce the same pattern as a narrow opening of the same width. 1. Take a hair from someone in your group. Stretch the hair and tape it down onto the plastic lens holder. Mount the holder onto the track. 2. Position the laser so that it shines on the hair and creates a pattern similar to what you saw for a narrow slit. 3. Measure the distance between the hair and the screen. 4. Determine the distance (y) between the middle of the central bright fringe and the middle of the first dark fringe on one side of the pattern (as shown in the diagram above). It is easier to measure the distance between the centers for the dark fringes on either side of the central bright fringe and divide that distance by two. 5. Calculate the width of the hair.

3 Activity 2: Two-Slit Interference When laser light passes through a double slit, the interference pattern consists of bright fringes of equal widths. The difference in the distances from the two openings to a spot at an angle off center is d sin, where d is the separation between the slits. The centers of the bright fringes are located at angles where this difference is 0,, 2, etc. (constructive interference) and the centers of the dark fringes are located at angles where the path difference is /2, 3 /2, etc. (destructive interference). These two conditions give: bright fringes: dark fringes: sin m m d m = 0, 1, 2, sin m m 1 2 /d m = 0, 1, 2, The brightness of the pattern varies because of the width of the individual slits. NOT TO SCALE y 2 y 1 Pattern 1 L 2 d Experiment You will use an interference pattern to determine the distance between the two narrow slits. 1. Set up the red laser to pass through a pair of narrow slits with a separation of mm (either slit width is fine). The screen should be as far away as possible. Sketch the pattern that appears on the screen. Mark the middle of the pattern. (Note: Concentrate on the finer pattern which is due to the interference of light from the two slits.) Slits Question: How does the width of the central bright fringe compare with the widths of the other bright fringes?

4 Question: How does the brightness of the fringes vary? 2. Measure the distance between the slits and the screen. L = 3. Measure the distances (y) between the middle of the central bright fringe and the middles of the next three bright fringes in the pattern. Enter the measurements in the second column of the table below. Bright Fringe 1 st 2 nd 3 rd y = Distance to bright fringe (m) = Angle to bright fringe dexp = slit separaton (m) 4. For each bright fringe, calculate the angle from the middle of the central bright fringe. (Hint: Sketching what you measured will be helpful again.) Enter the results in the third column of the table above. Show your first calculation.

5 5. For each bright fringe, use the known wavelength of the red laser (650 nm) and your measurements to calculate the experimental separation (dexp) between the slits and enter the results in the fourth column of the table above. Show each calculation. 6. Calculate the average of the experimental separation between the slits found in step 5. davg = Question: How does the average experimental slit separation compare to the value written on the slide (note, compare against the appropriate slit separation )? Calculate the percent difference. Question: Qualitatively, how do you expect the double-slit interference pattern to change if a green laser ( = 540 nm) is used instead of a red laser? Assume everything else about the setup remains the same. Explain your reasoning.