81. (a) The central diffraction envelope spans the range –θ1<< +1where 11sin ( / )aθλ−=which could be further simplified ifthe small-angle approximation were justified (which it is not, since ais so small). The maxima in the double-slit pattern are at mmd=−sin,1λso that our range specification becomes 111sinsinsin,mada−−−λλλ⎛⎞⎛ ⎞−<<+⎜⎟⎜ ⎟⎝⎠⎝ ⎠which we change (since sine is a monotonically increasing function in the fourth and first quadrants, where all these angles lie) to .maλλλ−<<+Rewriting this as -d/a < m< +d/awe arrive at the result –7 < m< +7 which implies (since mmust be an integer) –6 <m<+6 which amounts to 13 distinct values for
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This note was uploaded on 06/03/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.