Scan10010 - Physics 7C(b While light waves don’t diffract...

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Unformatted text preview: Physics 7C (b) While light waves don’t diffract through doorways, sound waves do, since we can hear sounds that are around a corner from us. What does this imply about the typical wavelength of sound? [P4] Using the small-angle approximation, show that the first several interference maxima of any grating are spaced at regular intervals on the screen. Show the same thing for the first several diffraction minima. Find the ratio of the spacing interval for interference maxima to that for diffraction minima, in terms of a and d. There’s a good reason why this ratio must be less than one for all gratings, which implies that interference maxima are always more closely spaced than diffraction minima. What is the reason? (Hint: try to draw a picture of a grating with this ratio greater than one.) [P5] Suppose the mth interference order is missing because it coincides with the nLh diffraction minimum for a particular grating. What is the ratio of slit width to slit separation for this grating? IV. Procedure Measuring Slit Width and Spacing Align the diode laser along the optical bench, turn it on, and shine it through one of the one-slit gratings on the 3”x5” grating plate. You should see a grating spectrum with many bright orders. [Q1] Do the orders you are seeing arise from interference, diffraction or both? How do you know? Choose one of the bright spots and count which order it is. Measure its angular position on the screen and from this information deduce the slit width of your grating. (Because the orders are fuzzy, you may have some measurement error in determining their position; you can reduce this by picking a high order to measure or by using the lens.) [QZ] How close is your calculated a to the given value? [Q3] PREDICT: How will the spectrum change if you use a one-slit grating with a different value of the slit width? Sketch your prediction. To test your prediction, shine the diode laser through several other one—slit gratings and observe what happens to the spectrum on the screen. [Q4] Was your prediction correct? If not, what happened? Now shine the laser through a double-slit grating. Observe the spectrum. DIFFRACTION GRATINGS 10 50 ...
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