A radar operating at a wavelength of 4 cm is to have a resolving power of 34 m at a range of 2 km. Find the minimum width its antenna must have. Round your final answer to two decimal places.

Answer 1

Resolving power θ in arc seconds is given by 206265 * 1.22 λ/D. Solve for diameter D = 206265 * 1.22 λ / θ. Wavelength λ is 0.04 m. For small angles, which certainly applies here, θ (in radians) = sin θ = opp/hyp = (34 m)/(2000 m) = 0.017 radians. One radian = 180/π degrees, and when you multiply this by 60 minutes of arc per degree and 60 seconds of arc per minute, that conversion is the 206265 number above. So we can leave out the conversion to arc seconds and leave θ in radians.

So diameter D = 1.22 λ/θ = (1.22)(0.04)/(0.017) = 2.87 m.