Path Difference

In the double slit experiment, a coherent light source is split into two light waves, and these two waves interfere with a phase determined by the difference in distance traveled. Assume a set of slits located a distance D from a screen as shown above. At a given point on the screen a distance x_m from the center line corresponding to an angle

of q_m, the path difference between the two waves will be approximately d·sin q_m, which for the small angles usually encountered, can be approximated as d·q_m, with the angle q_m in radians.