Microwave Experiments Fred, Geoff, Lise,and Phil

Intensity vs. Angle S Probe

Basic Optics n Reflection –Angles –Standing Waves Speed of light: c=  =(freq*(x/nodes)*2) Speed of light: c=  =(freq*(x/nodes)*2) n 10.5 ±.1 Ghz -> 3.01E8±.03E8 m/s (typical) M S   S Probe: Count Nodes in x x

Intensity n Point Source: I~1/r 2 n Our Source: I~1/r r MS

Refraction Through a Prism n Use prism n See handout for experiment diagram n Measure the angle of maximum intensity n Using this angle and Snell’s Law, calculate the index of refraction of the Prism n n = 1.46

Polarization n Polarization: Direction of E-field n Our source and receiver are polarized –Only projection of E onto polarization of receiver is detected: E received ~ cos (  ) Intensity ~ cos 2 (  ) Intensity ~ cos 2 (  )  Source Polarization Received Signal Receiver Polarization S M

Interference n Path Difference –Wave is f(kx-  t) –Implies Phase Diff.  =k  = (2  / ) f (z/d)=f sin(  )  =k  = (2  / ) f (z/d)=f sin(  ) Effect of  Effect of  –E~sin( kx-  t-.5 k  ) + sin( kx-  t+.5 k  ) = 2 sin( kx-  t) cos(.5 k  ) –I~E 2 –I~ cos 2 (.5 k  ) = cos 2 (.5 k f sin(  ) ) d f   z d>>f -> sin(  )->tan(  ) So  = f (z/d) 

Double Slit Interference n Diffraction Effects –Intensity from each source varies as sin 2 (  )/  2, where  =.5 k w sin(  ), w=slit width –So I~ sin 2 (.5k sin(  ) w) cos 2 (.5k sin(  ) f) /(.5 k sin(  ) w) 2 n Prediction –Black: Diffraction –Blue: Diff. + Interference  I f = 2 w

Double Slit Results n Results –Envelope and Interference –Limit of Resolution of Angle? M S Mirror Extension

Single Slit Diffraction n Used various slit widths and measured intensity verses angle sin(  ) = n sin(  ) = n /a S Mirror Extension M a

Single Slit Diffraction

Lloyd’s Mirror n Premise –Two ways to reach detector n Off of mirror or straight line –Path difference implies interference 2*(Distance Between Maxima)= 2*(Distance Between Maxima)= n Results –Wavelength: n 2.5 ±.7 cm –c=2.6E8 m/s ±.3E8 m/s SM

Fabry-Perot Interferometer n Changing the interference pattern between two partial reflectors allows us to measure the wavelength. n See handout for experiment diagram (d2 – d1)/M = (d2 – d1)/M = We measured = 2.62 and We measured = 2.62  0.1 and = 3 = 3  0.1

Michelson Interferometer n n Setup – –Beam Splitter – –Path Difference->Interference n n Results – –Wavelength= S M

Fiber Optics n Using tube filled with styrene pellets, we noticed higher transmission levels n Although very sensitive to positioning, the signal was rather constant with different curvatures

Bragg Diffraction n Bragg’s law give us a way to measure distances between crystal planes d sin  = n /2 where d is the distance between crystal planes d sin  = n /2 where d is the distance between crystal planes

Frustrated Total Internal Reflection n Setup n Is there any transmission to 2? S M 1 2

Lenses S