Chapter 46: Problem 22

Question: A navy cruiser employs radar with a wavelength of $\lambda~=~1.57~{\rm cm}$. The circular antenna has diameter of $a~=~2.33~{\rm m}$. At a range of $d~=~6.25~{\rm km}$, what is the smallest distance that two speed boats, hcan be from each other and still be resolved as separate objects by the radar system.

Solution: The electromanetic radiation reflected from the speed boats is focused by the circular antenna, and so the circular antenna acts like a circular hole in a mask, with an incident plane wave. Therefore, the diameter of the antenna, as the diameter of the circular hole, that we are used to dealing with. $a\sin\theta~=~1.22\lambda$, and hence $h~=~{1.22\lambda\over a} d~=~ 51.4~{\rm km}$.