Chapter 45: Problem 4

Question: Find the slit separation of a double slitarrangement that will produce bright interference fringes 1.00^o apart in angular separation. Assume a wavelength of $\lambda~=~592~{\rm nm}$.

Solution: As the angular separation between the fringes is small, in the forward direction $\theta\sim 0$, we can make the small angle approximation $\sin\theta\sim\theta$. The location of each maximia is determined by $d\sin\theta~=~m\lambda$, where m is an integer. Using the small angle approximation, and taking the difference between the m'th and the (m+1)'th fringe, we have $d\left(\sin\theta_{m+1}-\sin\theta_m\right)~=~\left( m+1-m\right)\lambda$, which yields $d\ \delta\theta~=~\lambda$. Inserting the value of $\delta\theta~=~1.00^o$, and $\lambda~=~592~{\rm nm}$gives $d~=~3.4\times 10^{-5}~{\rm m}$.