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Question

A circular radar antenna on a Coast Guard ship has a diameter of 2.10m and radiates at a frequency of 15.0GHz. Two small boats are located 9.00km away from the ship. How close together could the boats be and still be detected as two objects?

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Solution

We are given D=2.10m and L=9000m. The wavelength of the Coast Guard radar is
λ=cf=3.00×108m/s15.0×109Hz=0.0200m
From Rayleigh's criterion, θmin=1.22λD=dL. Therefore,
d=1.22[(0.0200m)(9000m)2.10m]=105m

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