Single Slit Diffraction

Transcription

1 Name: Date: PC1142 Physics II Single Slit Diffraction 5 Laboratory Worksheet Part A: Qualitative Observation of Single Slit Diffraction Pattern L = a 2y 0.20 mm 0.02 mm Data Table 1 Question A-1: Describe what happens to the spatial extend and overall brightness of the central peak as the slit width becomes narrower. Explain the observed trend qualitatively according to theoretical consideration. Question A-2: The two first minima are symmetrically positioned on both sides of the reference line at θ = 0 and located at the angle θ 1 determined by the criterion: a sin θ 1 = λ. Show that the angular spread of the central peak θ can be approximated as θ 2λ/a. Hence, or otherwise, show that as the slit width is decreased from a = 0.20 mm to a = 0.02 mm, the angular spread of the central peak θ increases by a factor of 10. Page 1 of 6

2 Single Slit Diffraction Laboratory Worksheet Page 2 of 6 Analysis A-1: The angular spread of the central peak θ can be approximated as θ 2y/L radians. Based on your data in Data Table 1, determine the angular spread of the central peak θ for each slit width. Are your results consistent with the prediction that θ will be ten times larger when a = 0.02 mm than when a = 0.20 mm? Analysis A-2: Determine the angular spread of the central peak using the formula θ 2λ/a for each slit width. Compare these values with your experimental findings using percentage discrepancy. Part B: Quantitative Observation of Single Slit Diffraction Pattern I 0 = Secondary Maxima y left I left y right I right First Second Third Forth Data Table 2

3 Single Slit Diffraction Laboratory Worksheet Page 3 of 6 Question B-1: The spatial pattern of light intensity produced by a light wave passing through a single rectangular-shape slit is given by equation (6). Show that the angular locations and intensities of the secondary maxima are: Secondary Maxima Angular Position Intensity First sin θ 1 = λ/a I 1 = 0.047I 0 Second sin θ 2 = λ/a I 2 = 0.016I 0 Third sin θ 3 = λ/a I 3 = 0.008I 0 Forth sin θ 4 = λ/a I 4 = 0.005I 0 Analysis B-1: For each secondary maxima: (1) determine the average distance from the central peak; (2) determine the angular location sin θ; (3) compare the experimental angular location sin θ with theoretical value using percentage discrepancy; and (4) determine the average intensity and compare it with theoretical value using percentage discrepancy. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report.

4 Single Slit Diffraction Laboratory Worksheet Page 4 of 6 m y left y right Data Table 3 Question B-2: Use equation (6) to show that the angular locations θ m of the minima are given by a sin θ m = mλ where m = 1, 2, 3, 4,.... Analysis B-2: For each minima, determine the average distance from the central peak and the angular position sin θ m. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report.

5 Single Slit Diffraction Laboratory Worksheet Page 5 of 6 Analysis B-3: Perform a linear least squares fit to your data with the angular position of the minima sin θ m as the vertical axis and m as the horizontal axis. Plot a graph of angular position of the minima sin θ m against m. Also show on the graph the straight line that was obtained by the linear least fit to the data as well as the error-bar of your data. Be sure to attach a copy of the graph (with the spreadsheet) to your laboratory report. Gradient: ± y-intercept: ± Correlation coefficient: Analysis B-4: The gradient of the plot sin θ m against m is λ/a. Determine the experimental value for the slit width a given that the wavelength of the laser is λ = 650 nm. Compare it with the manufactured value using percentage discrepancy. Experimental value: ± Manufactured value: % discrepancy = % Part C: Diffraction Pattern of A Human Hair L = d = m y left y right Data Table 4

6 Single Slit Diffraction Laboratory Worksheet Page 6 of 6 Analysis C-1: For each minima, (1) determine the average distance from the central peak and the angular position sin θ m ; and (2) determine the thickness of the hair strand a. Show a sample calculation and be sure to attach a copy of the spreadsheet to your laboratory report. Analysis C-2: Estimate an experimental value for the thickness of your hair strand d and its associated uncertainty with the appropriate number of significant figures. Compare your experimental value with the measured value using percentage discrepancy. Show your work. Experimental value: ± % discrepancy = % 6 Laboratory Report Submit a laboratory report by ONE week after your laboratory session. Important: Before leaving the laboratory, have a demonstrator initial on your data table(s)! Last updated: Thursday 16 th October, :18am (KHCM)