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### Lab 7

Course: PHYS 2Cl, Winter 2012
School: UCSD
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Word Count: 804

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Werry Partner: Christopher Sharon Xu 3/6/12 Lab 7 Wed 9AM 2.1 Boundary Conditions Q: Consider a light ray in air, whose index is essentially 1.00 (that of vacuum), normally incident on a sheet of glass, for which, typically, n2 = 1.5. What fraction of the initial intensity is reflected? lref/I0 = 3.2 Measuring 0 in Free Space with Interference Methods: Method from the lab manual was followed except for the...

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Werry Partner: Christopher Sharon Xu 3/6/12 Lab 7 Wed 9AM 2.1 Boundary Conditions Q: Consider a light ray in air, whose index is essentially 1.00 (that of vacuum), normally incident on a sheet of glass, for which, typically, n2 = 1.5. What fraction of the initial intensity is reflected? lref/I0 = 3.2 Measuring 0 in Free Space with Interference Methods: Method from the lab manual was followed except for the following alteration: the distance between the transmitters to the reflector was not measured to be exactly an integer number of wavelengths. This precaution did not need to be taken to determine accurate results, because the wavelength would still be the same. Data: Error in measurements was taken to be 0.2cm. 0.1cm from ruler uncertainty and 0.1cm from the microwave transmitter error range. max(+/d (+/min(+/d(+/0.2cm) 0.2cm) 0.2cm) 0.2cm) 30.7 31.6 32.1 33 1.4 1.4 33.5 1.4 34.3 1.3 (+/- 0.2cm) 2.8 2.7 Analysis: Q: What is the wavelength of the microwave with the frequency 10.525 GHz? Q: Would it be better to measure the distances between successive minima and average them or to measure the distance between pairs of minima separated by several wavelengths? It is better to measure the distances between pairs of minima rather than successive minima. With pairs of minima there is only one measurement to introduce uncertainty. With successive minima, each minima introduces a new source for error as seen by error propogation. Q: How well does the specified frequency (wavelength) agree with your measurements? Given this low t-value (<1) we can accept our measured wavelength. 3.3 Determining the Index of Refraction Methods: The above set-up was created with the goniometer connecting the receiver to the transmitter. The transmitter was pressed against the prism to reduce error introduced by the shifting transmission angle. The corresponding angle theta on the prism was measured. The goniometer angle was adjusted by shifting the transmitter until a maximum transmitter reading was displayed. A maximum and minimum angle for the same reading was recorded to incorporate uncertainty. Data: Regular: 159.2 < 1< 164.1 1 = 161.7 +/- 2.5 Inverted: 159.8 < 2 < 161.9 2 = 160.9 +/- 1.1 Analysis: Q: To which medium do n1 and n2 correspond? Which one do you know already? n1 is the medium of the slab, n2 is the air which is known to be 1.000. Q: Calculate the index of refraction of slabs. n1sin() = n2sin() = = 180- + where n2 is the medium of air = 1.000 Regular: Flipped: 1.45 +/- 0.04 [+/- 0.04 from sin(+/-2.5)] = 1.48 +/- 0.02 Since the second has result less error, we will use this as our final result. Q: Determine the wavelength in free space based on index of refraction and wavelength in the slab. Using equation 2 and the results from section 3.3 and 3.4 find o. nslabslab = nairair slab = 2.07 +/- 0.1 cm (from 3.4) air = cm Q: Compute the t-value between the expected wavelength to that inferred from index of refraction of slabs and wavelength in slab. air = 2.85 +/- 0.14 cm [from 3.2] A t-value of this magnitude suggests some major error present in the measured value. See conclusion. 3.4 Measuring in Material with Interference Methods: Method was followed from the lab manual. Data: Wavelength is calculated by measuring the distance between maxima, which is called m. nod w (+/m(+/e 0.01cm) 0.01cm) 1 17.12 0 2 16.09 1.03 3 15.03 2.09 4 14.02 3.10 The graph of n vs. m has a slope of 2/, so we can find the wavelength by dividing 2 by the slope. Analysis: Q: Why does the detector find alternating maximum and minimum values as you vary the thickness of the slabs? Altering the thickness of the slabs changes the distance between the emitter and the reflected surface. Since the wavelength does not change, the detector is measuring the shift in the wave pattern by the change in distance; thus it measures nodes and anti-nodes as you change the thickness. Q: Let us assume that you cannot find m = 1 as a reference point to begin your measurements. The best you can do is find a single maximum value and start consecutive measurements there. Starting at an arbitrary point and counting will change the functional form you will plot. How will d = (1/2) m change? The slope of the line will not change, therefore 2/ = m/d will not change, though d will change proportionally to m. Since m does not equal 1 for our reference point, d will be offset by a factor of m. Conclusion The large discrepancy causing the large t-value in section 3.3 is due to both the inaccuracy of the measured wavelength through the material from 3.4 and the angle measurements that were used to determine the index of refraction of the slab. Opportunity for error is present in the angle measurements and the distance measurements between maxima, as well as the systematic error introduced by the transmitter and receiver. Given these sources for error, perhaps the uncertainty value for calculating the t-value should have been larger. A possible way to decrease error would have been to take more measurements for section 3.4. In section 3.3, the large variances in angles also introduced error due to the imprecise measuring of the receiver.
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