Chapter 27, Problem 18PE

Figure 27.56 shows a double slit located a distance x from a screen, with the distance from the center of the screen given by y. When the distance d between the slits is relatively large, there will be numerous bright spots, called fringes. Show that, for small angles (where $\text{sin}\theta \approx \theta$, with $\theta$ in radians), the distance between fringes is given by $\Delta y=x\lambda /d$.

Figure 27.56 The distance between adjacent fringes is $\Delta y=x\lambda /d$, assuming the slit separation d is large compared with $\lambda$.