6. Wave Optics: Radioastronomy Figure 3: Two radio antennas transmit, receive and interfere. Two radio antennas are separated by a distance d and radiate at a wavelength A. For simplicity assume that each antenna by itself would radiate equally in all directions. (a) [5 points] Consider rays that propagate in the direction 9 shown in the gure. What is the extra distance that rays from antenna B must travel compared to rays from antenna A? Give your answer in terms of d and 9. (b) 12 points] The intensity in any particular direction is determined by interference between the two antennas. Assuming that the antennas are driven in phase the intensity is maximum when the extra distance calculated in part (a) is an integer multiple of the wavelength A. Use this criterion to write down a condition that must be satised by sint? in order for the intensity in that direction to be a maximum. Also assuming that A/d = 1/3 numerically calculate all values of 9 that satisfy this condition and that lie in the range ar/2 5 6 5 7r / 2. (c) [3 points] Now suppose that the two antennas are not driven in phase. Assume that the signal that drives antenna B is delayed relative to the signal that drives antenna A. The effect of this delay is to add to the geometric difference between the path lengths calculated in part (a). Assuming that the effective extra distance added to rays from antenna B is a half wavelength, what intensity do you expect to see at the angles calculated in part (b)