Conceptual Physics (12th Edition)

The equation at the bottom of page 550 explains this. $$\lambda = d sin \theta$$ Suppose we use a longer wavelength, $\lambda$. The left-hand side of the equation is larger, so the right-hand side must be larger too. The distance between the slits, d, is fixed. The longer wavelength gives a more spread-out pattern, i.e., $\theta$ increases, because sin $\theta$ increases. Alternatively, use Figure 29.18. The bright fringes are seen when there is a full-wavelength difference in path lengths from the two slits. With a long red wavelength, one has to move farther from the centerline to have a full-wavelength path difference. The pattern is more spread out.