The radar system of a navy cruiser transmits at a wavelength of 1.6 cm, from a circular antenna

step 1 36 .20, we're told that the radar system of a Navy cruiser uses radio waves of this wavelength.

The radar system of a navy cruiser transmits at a wavelength...

The radar system of a navy cruiser transmits at a wavelength of $1.6 \mathrm{cm},$ from a circular antenna with a diameter of 2.3 $\mathrm{m} .$ At a range of $6.2 \mathrm{km},$ what is the smallest distance that two speedboats a can be from each other and still be resolved as two separate objects by the radar system?

The radar system of a navy cruiser transmits at a wavelength of $1.6 \mathrm{cm},$ from a circular antenna with a diameter of 2.3 $\mathrm{m} .$ At a
range of $6.2 \mathrm{km},$ what is the smallest distance that two speedboats a
can be from each other and still be resolved as two separate objects
by the radar system?

Key Concepts

Antenna Aperture

The antenna aperture, typically defined by parameters like the diameter of a circular antenna, directly influences the system’s resolution. A larger aperture usually enables a narrower beam width, enhancing the radar’s ability to distinguish between closely spaced objects.

Angular Resolution

Angular resolution refers to the minimum angle between two distinct objects that an imaging system, such as a radar antenna, can separate. It is directly related to the Rayleigh criterion and depends on the wavelength of the signal and the size of the aperture.

Spatial Resolution

Spatial resolution in a radar context is the minimum distance between two objects at a particular range at which the radar can distinguish them as separate. It is determined by translating the angular resolution, given by diffraction and antenna properties, into a linear dimension based on the distance to the objects.

Diffraction Limit

The diffraction limit describes the fundamental limit on the resolving power of any electromagnetic system due to the wave nature of light or radio waves. It means that even with perfect optics or antennas, waves spread out and interfere in such a way that sets a lower bound on how close two objects can be while still being differentiated.

Rayleigh Criterion

The Rayleigh criterion is a practical rule for determining the minimum angular separation of two point sources that can just be resolved, given by the wavelength and the aperture size. It is widely used in optics and radar systems to estimate the resolving capabilities limited by diffraction.

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