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)