What are the two equations for divergence angle?

What are the two equations for divergence angle?

• A. Sin divergence angle = 1.85/Diameter(mm) x frequency(MHz); Sin divergence angle = 1.2 x wavelength/ Diameter
• B. Sin divergence angle = 1.2 x wavelength/ Diameter; Sin divergence angle = 1.85/Diameter(mm) x frequency(MHz)
• C. Sin divergence angle = 1.85 x frequency / Diameter(mm); Sin divergence angle = 1.2 x wavelength / Diameter
• D. Sin divergence angle = frequency/Diameter; Sin divergence angle = wavelength/Diameter

Answer: (A)

The divergence angle of a beam from an aperture depends on the ratio of the wavelength to the aperture diameter: bigger diameter or shorter wavelength produces a narrower beam. For a circular aperture, the basic relationship is that the sine of the divergence angle scales with λ/D, with a constant that depends on how exactly you define divergence (first null, half-power, etc.). Two common practical forms use different unit conventions but express the same idea. If you express the aperture diameter in millimeters and the frequency in megahertz, you get a form where the sine of the divergence angle is proportional to the frequency divided by the diameter, with a constant around 1.85 that arises from the unit conversions and the specific divergence definition used. If you express the measure in terms of the wavelength directly, you get a form where the sine of the divergence angle is proportional to the wavelength divided by the diameter, with a constant around 1.2. These are just two convenient ways to write the same underlying relationship, chosen to fit common unit systems in practice.

The divergence angle of a beam from an aperture depends on the ratio of the wavelength to the aperture diameter: bigger diameter or shorter wavelength produces a narrower beam. For a circular aperture, the basic relationship is that the sine of the divergence angle scales with λ/D, with a constant that depends on how exactly you define divergence (first null, half-power, etc.).

Two common practical forms use different unit conventions but express the same idea. If you express the aperture diameter in millimeters and the frequency in megahertz, you get a form where the sine of the divergence angle is proportional to the frequency divided by the diameter, with a constant around 1.85 that arises from the unit conversions and the specific divergence definition used. If you express the measure in terms of the wavelength directly, you get a form where the sine of the divergence angle is proportional to the wavelength divided by the diameter, with a constant around 1.2. These are just two convenient ways to write the same underlying relationship, chosen to fit common unit systems in practice.