("counting minima of two coherent sources.") this problem is an extension of the example of two coherent sources we discussed in class. two coherent point sources (let us call them s1 and s2) emit identical radio waves in phase at wavelength λ. s1 is positioned at (0, −d/2) and s2 is at (0, +d/2). a radio detector is placed very far away (compared to d) and can move on a large circle with respect to the coordinate origin and scan the interference pattern from the combination of waves from both sources.

(a) the radio detector is receiving the waves from both sources at angle θ with respect to +x-axis. what is the difference in path length, ∆l, between the waves coming from the two sources?

(b) given path difference ∆l, what is the phase difference at the detector?

(c) when the detector is on the x axis (both positive and negative), is it observing a minimum, or a maximum?

(d) the detector scans the full circle, and finds 30 points of zero intensity (minima), including two on the y-axis, one of them above the sources and the other one below the sources. what is the value of d/λ?