A radar for tracking aircraft broadcasts at 12 GHz microwave beam from a 2.0mdiameter circular radar antenna. From a wave perspective the antenna is a circular aperture through which the microwaves diffracts.
A. what is the diameter of the radar beam at a distance of 30 km?
B. if the antenna emits 100 kW of power what is the average microwave intensity at 30 km?
1 Answers

A. Thewavelengthofthewaveis,\\ \lambda =\frac{c}{f} \\ =\frac{3 \times 10^{8} \mathrm{~m} / \mathrm{s}}{12 \times 10^{2} \mathrm{~Hz}} \\ =0.025 \mathrm{~m} \\ =25 \mathrm{~mm}\\ Theangularresolutionofthesystemis,\\ \sin \theta=1.22\left(\frac{\lambda}{D}\right)\\ =1.22\left(\frac{25 \mathrm{~mm}}{2 \mathrm{~m}}\right)\\ \theta=\sin ^{1}(0.01525)\\ =15.25 \mathrm{mrad}\\ Thediameteroftheradarbeamfromthehalfangleis,\\ d=2(15.25 \mathrm{mrad})\left(30 \mathrm{~km}\left(\frac{1000 \mathrm{~m}}{1 \mathrm{~km}}\right)\right)\\ =915 \mathrm{~m}\\ \\