The Michelso Iterferometer Ady Chmileko, 0310799 Istructor: Jeff Gardier Sectio 1 (Dated: :30 pm Tuesday October, 013) I. PURPOSE The purpose of the experimet is to use the Michelso Iterferometer, oce calibrated, to measure the wavelegth of mercury (Hg) gree light, as well as measure the separatio of the Hg yellow lies. We will also use the Michelso Iterferometer alog with a small vacuum chamber to determie the approximate refractive idex of air ad compare it to our predictios of light travellig through a medium compared to a vacuum. We will also observe the iterferece patter of white light ad try to apply theory to our observatios. II. ANALYSIS A. Calibratio of the Iterferometer i Sodium (Na) Yellow Light D 1 (± 0.005 mm) D (± 0.005 mm) K 5.000 5.160 0.184 ± 0.011 6.50 6.400 0.1964 ± 0.0137 TABLE I: Measuremets made for the displacemet of the micrometer for 100 diffractio lies ( ) of Na yellow light. Sample Calculatios for K usig row 1 of Table I usig a λ of 5893Å K = λ ( (D 1 D ) K = 100 5893Å ( (5.000 5.160) K = 0.184 Sample Calculatios for K usig row 1 of Table I K = K ( D) D 1 D + ( ) ( 0.005) K = 0.184 0.16 + () 100 K = ±0.011 Sample Calculatios for K usig row 1 of Table I. i K = Ki K = 0.184+0.1964 K = 0.1903
Sample Calculatios for K usig row 1 of Table I. i Ki K = K = 0.011+0.0137 K = ±0.019 K was foud to be 0.1903 ± 0.019, takig 0.005mm as the ucertaity i the micrometer measuremet ad as the ucertaity, misreadig at most the positio of the first couted ad last couted diffractio lies. B. Determiatio of the Wavelegth of the Mercury (Hg) Gree Light D 1 (± 0.005 mm) D (± 0.005 mm) λ (m) 6.300 6.445 551.9 ± 53.4 3.090 3.30 53.8 ± 5.5 TABLE II: Measuremets made for the displacemet of the micrometer for 100 diffractio lies ( ) of Hg gree light. Sample Calculatios for K usig row 1 of Table II usig a λ of 5893Å λ = K ( (D1 D) λ = 0.1903 ( (6.300 6.445) 100 λ = 551.9m Sample Calculatios for λ usig row 1 of Table II λ = λ ( D) λ = 551.9 D 1 D + K K ( 0.005) 0.145 + (0.019) 0.1903 λ = ±53.4 Sample Calculatios for λ usig row 1 of Table II. i λ = λi λ = 551.9+53.8 λ = 54.35 Sample Calculatios for λ usig row 1 of Table II. i λi λ = λ = 53.4+5.5 λ = ±53.0 Sample Calculatios for % deviatio of observed measured wavelegth of gree light from Hg with the accepted value of 546.074 m % deviatio = 546.074 54.35 546.074 100% % deviatio = 0.7% λ for the gree light emitted by Hg was foud to be 54.35 ± 53.0 m, which oly differed by 0.7% from the accepted value of 546.074m ad was well withi our calculated ucertaity.
3 Separatio of the Hg Yellow Lies D 1 10 (± 0.005 mm): 3.330, 3.740, 4.140, 4.570, 4.980, 5.380, 5.810, 6.0, 6.630, 7.050 δd 1 9 (± 0.005 mm): 0.410, 0.400, 0.430, 0.410, 0.400, 0.430, 0.410, 0.410, 0.40 Sample Calculatios for δd i δdi δd = δd = 0.410+0.400+0.430+0.410+0.400+0.430+0.410+0.410+0.40 9 δd = ±0.413 Sample Calculatios for δd δd = ± δd δd = ± 0.005 9 δd = ±0.0036mm Sample Calculatios for λ λ usig λ as 578.0 m λ λ = λ K δd λ λ 578.0m = 0.1903 0.413mm λ λ =.15m Sample Calculatios for (λ λ ) (λ λ ) = λ λ (λ λ ) =.15m ( K K ) ( δd δd ) ( 0.019 0.1903 ) ( 0.0036 0.413 ) (λ λ ) = 0.14m Sample Calculatios for % deviatio of observed measured wavelegth differece of Hg Yellow I ad II lies with the accepted differece of 579.065m-576.959m =.106m % deviatio =.106.15.106 100% % deviatio = 0.9% λ λ for the Hg Yellow I ad II lies was measured to be.15 ± 0.14m, which oly differed by 0.9% compared to the accepted values of 579.065m-576.959m =.106m, the accepted value was also withi our estimated ucertaity. C. The Idex of Refractio of Air (for Na Yellow Light) P 0 (± 0.5 cmhg) P i (± 0.5 cmhg) 75.0 5 66.0 58 48 39 30 14 74.0 5 65 56.5 49 41 33 4 15 7 74.0 5 65 60 50 41 31 1 13 TABLE III: Measuremets take recordig the cell pressure P i for each iterval of 5 ( ) rigs disappearig.
4 FIG. 1: Refractive idex of air - 1 versus the iteral cell pressure i mmhg show i blue. 3 outlier values idicated i red are ot used i the regressio. Sample Calculatios for air usig regressio costats a = 6.81 10 7 ad b = 0.000343 at stadard atmosphere pressure of 760mmHg for Na yellow light air 1 = ax + b air 1 = 6.81 10 7 760mm + 0.000343 air = 1.00034 Sample Calculatios for air air = ( air 1) air = 0.00034 ( a a ) ( b b ) (.54 6.81 ) ( 6.53 343. ) air = 0.00013 Usig the regressio costats a ad b idicated i Fig.1, we ca calculate the refractive idex i air for Na yellow light (5893Å) at stadard atmospheric pressure (760 mmhg) was foud to be 1.00034 ± 0.00013 which is cosistet with theory as it should be greater tha 1 (refractive idex at a vacuum). D. Observatio of White Light Friges Trial 1: D 1 = 14.14 ±0.005 mm Trial : D 1 = 14.14 ±0.005 mm D = 14.11 ±0.005 mm D = 14.11 ±0.005 mm Sample Calculatios carriage distace travelled. δd carriage = K δd micrometer δd carriage = 0.1903 (14.14mm 14.11mm) δd carriage = 5.709 10 6 m
5 Sample Calculatios for δd carriage δd carriage = δd carriage ( D) δd carriage = 5.709µm ( 0.005) δd carriage = 0.34µm D 1 D + K K 0.03 + 0.019 0.1903 The white light friges was observed to be a white bad, with a purpler colour, the blue, gree, yellow, orage, red, the the patter bega to repeat i the fashio. The approximate distace over which friges are observed was betwee 14.14 mm ad 14.11 mm o the micrometer, which traslates to 5.709 µm of actual carriage distace. Frige diameters are so large ear zero path differece because the iterferece patter is a result of a superpositio of wave crests, at ear zero path differece the wave crests is small so the for two crests or troughs to alig up takes a greater agle, or larger diameter friges. You ca see so may colours because the white light from the icadescet bulb cotais all (or most) of the wavelegths of light, as certai parts of the light iterfere with each other as the carriage is moves, other wavelegths costruct resultig i the separatio of colours cotaied withi the white light. Whe the path legth is zero, that meas the path legth is the same for all wavelegths ad that is where the patter appears early black. At large optical path differeces the radom separatio of all the wavelegths ad the o-exact aligmet of the mirrors you caot observe the vibrat colours except ear zero path legth differeces. III. CONCLUSION First the iterferometer was calibrated ad the costat K was foud, relatig the micrometer movemet to the actual carriage travel of the mirror ad usig a kow source wavelegth was foud to be 0.1903 ± 0.019, ad this value was used throughout for the rest of our calculatios. Usig the same method above with the measured K, we measured the wavelegth of the gree like spectral lie of Hg, ad foud it to me 54.35 ± 53.0 m, which oly differed by 0.7% of the accepted value of 546.074 m, which is also withi out ucertaity estimates. Similarly we calculated the separatio of the Hg yellow lies. We measured the separatio to be.14 ± 0.14 m, which oly differed by 0.9% compared to the accepted value of.106 m. Usig a vacuum chamber ad by varyig the pressure (ad by extesio the umber of particles i the chamber), we were able to measure the refractive idex of air, air. Usig the Lorez-Loretz law we were able to plot our results ad calculate a umber for air at STP, 760 mmhg at room temperature for Na yellow light to be 1.00034 ± 0.00013. This is cosistet with theory as the refractive idex of materials should be greater tha 1 (the refractive idex of a vacuum).