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Unformatted text preview: N 2 j =1 e i (2 j- 1) = sin( N ) 2 sin Fig. 8. The case N = 7 and b . N 2 j =1 F j = 2 b sin sin( N ) 2 sin = b sin sin( N ) sin P = E L r e i ( kr- t ) b sin sin( N ) sin and the intensity is I * P P = E L r b 2 sin 2 diffraction off wide slit sin( N ) sin 2 interference of N point sources which is the result we were seeking. Notice that when N = 1 we reduce to the result on a single wide slit, and when N = 2 we reduce to the case of two wide slits. We get maxima from the interference part when = m , or, equivalently, a sin = m , i.e., a sin = m . Notice, that as N is integral, when = m so does N . Therefore when the denominator vanishes, so does the numerator, and at the limit sin( N ) / sin N as m . But for large N , N equals m more often then , so that the numerator vanishes also when the denominator does not. This gives us N- 1 minima between principal maxima, or N- 2 secondary maxima. Consider now the diffraction part, namely the sinc 2 function. Recall that := 1 2 kb sin = b sin . When b , the sinc function does not vary by much and effectively is constant 84 Fig. 9. The case N = 7 and b ....
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This note was uploaded on 07/19/2011 for the course PH 113 taught by Professor Liorburko during the Spring '09 term at University of Alabama - Huntsville.
- Spring '09