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Useful Relations for Midterm 3


    $\displaystyle I(\theta)~=~I_0 \cos^2\beta \left({\sin\alpha\over\alpha}\right)^2$  
       
    $\displaystyle I(\theta)~=~I_0 \left( {\sin N\beta\over N \sin\beta}\right)^2
\left({\sin\alpha\over\alpha}\right)^2$  
       
    $\displaystyle \beta~=~{\pi d \sin\theta\over\lambda}$  
       
    $\displaystyle \alpha~=~{\pi a \sin\theta\over\lambda}$  
       
    $\displaystyle a\sin\theta~=~m\lambda$  
       
    $\displaystyle d\sin\theta~=~m\lambda$  
       
    $\displaystyle a\sin\theta~=~1.22 \lambda$  
       
    $\displaystyle d\sin\theta~=~(m+{1\over 2})\lambda$  
       
    $\displaystyle r~=~\sqrt{m\lambda R}$  
       
    $\displaystyle 2 n d~=~m\lambda$  
       
    $\displaystyle 2 n d~=~(m+{1\over 2})\lambda$  
       
    $\displaystyle {1\over O} + {1\over I}~=~{1\over f}$  
       
    $\displaystyle m~=~{f_1\over f_2}$  
       
    $\displaystyle {\lambda\over a}~\gg ~{a\over R}$  
       
    $\displaystyle m~=~-{I\over O}$ (1)


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Martin Savage
1999-03-03