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waves04 - Problems and Home Experim en ts 529 Home experime...

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Problems and Home Experiments 529 9.3 5 Scotchlite. You ca n get a piece of red Scotcbliteadhesive tape in a hardware store. It is used for decorati ng, safety reflectors, bu bble chambers, etc. Look at it with a magnif ying glass. Ta pe a piece on a wall and shine a flashlight beam on it, wit h the flasWigh t held right in front of your nose so you see the light that is retr o- directed through 180 deg. Now gra duall y move the flashli ght out to the side while still shining the beam on the tape. Th at way )"ou can estima te the angular width of the retrodirected beam. Why do you expec t some angular width: i.e., why doesn't it give perfect retrodirection? 9.36 Coherence and polarizat ion. Light is emitted from an un polarized point source. First it passes through a linear polarizer with easy transmission axis at 45 deg to the x and IJ axes. Then it is incident on a double slit. Each slit is covered by a linear polariz er, one slit having th e polarization axis along X, the other having it along y. (0) Sup pose you look at the interference pattern with the unaided eye. Do you expect to have the usual two-slit interference pattern? Wh at do you expect? (b) Next suppose you look at the Interference pattern willie holding a polaroid linear polarizer in front of one eye. what do you expect to see? What hap pens as you rotate th e polaro id in front of your eye? (c) ow suppose )'ou look at the pattern thr ougb a circular polarizer run backward as an analyze r. what pattern do you expect to see? There are many nice variations you can make on this problem: (i) Put a right- hand ed circular polarizer ove r one slit and a left-handed circular polarizer over the other and repeat the above observations. [ii} Add a quart er- or half-wave plate just behind the slits, etc. 9.37 Double-slit interferometer. Suppose yOll cover o ne of tw o slits with a mic.ro- scope slide and th e other wi th nothin g. If the slide has thickness 1 mm, show that monochromatic light of wavelength 5000 A gets a retardati on in one slit of about 1000 wavelengths relative to the oth er. If the double-slit pattern is .not to wash out, tbe light must be fairly monochromatic. How narrow a ban d of wavelengths (in ang- stro ms) is required so that th e relative phase shift of the tw o slits varies by less than 180 deg from one edge of th e wav ele ngth band to the oth er? How could you use this fact to measur e the bandwidth of a spectral line? (\Vhat would you measure and plot versus what , and how would you obtain the bandwidth from the plot?) 9.38 Pinho le magnifier. Derive a fonnula for the magnification of a pinhole mag- nifier. Check the form ula as follows: Make two marks 2 em apart on one piece of paper; make two marks 2 mm apart on anoth er. Put th e pinh ole over one eye and nothing over the othe r. Both pieces of pape r should be illuminated from behind (at least, that is easiest to look at). With both eyes open , look with one eye through the pinhole al th e 2 mm mark s and with your oth er eye look at the 2 cm mar ks. Bring the 2 mm marks closer until you superpose the two sets of marks with your two eyes.
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waves04 - Problems and Home Experim en ts 529 Home experime...

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