Find the smallest resolvable angle of the 100 -m diameter...

Find the smallest resolvable angle of the 100 -m diameter Green Bank Telescope when it is observing radio waves at $20-\mathrm{cm}$ wavelength. What is its resolution when observing a $3-\mathrm{mm}$ wavelength?

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Key Concepts

Diffraction Limit

The diffraction limit is the fundamental constraint on the resolution of any imaging system due to the wave nature of light or other electromagnetic radiation. It sets the smallest angular separation that can be distinguished and is directly determined by the ratio of the wavelength of the radiation to the size (diameter) of the aperture.

Angular Resolution

Angular resolution refers to an instrument's ability to differentiate between two objects that are close together in the sky. It is often approximated by the formula ? ? ?/D, where ? is the minimal resolvable angle, ? is the wavelength, and D is the aperture diameter, assuming a diffraction-limited system.

Wavelength Dependency

The dependency on wavelength is crucial because the resolution improves (? decreases) with shorter wavelengths and degrades (? increases) with longer wavelengths. This means that telescopes observing at shorter wavelengths can achieve finer detail, while those observing at longer wavelengths, like radio waves, have more limited resolving power for the same aperture.

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