What is the smallest resolvable angle of the 2.4 -m Hubble Space Telescope when it is observing

step 1 Limit of graduation of the telescope is 1 .22 lambda by D. Here wavelength of light is 550 nanom

What is the smallest resolvable angle of the 2.4 -m Hubble...

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Key Concepts

Wavelength Dependency

The wavelength of light being observed directly influences angular resolution because the diffraction limit is proportional to the wavelength. Shorter wavelengths allow for finer resolution since the diffraction effects are minimized, whereas longer wavelengths result in a larger diffraction pattern and coarser resolution.

Diffraction Limit

The diffraction limit is a fundamental constraint in optics that sets the minimum angular separation at which two point sources can be distinguished. It arises from the wave nature of light and is typically expressed as the ratio of the observing wavelength to the telescope's aperture diameter.

Rayleigh Criterion

The Rayleigh criterion provides a specific formula to determine the diffraction limit for circular apertures. It indicates that the smallest resolvable angle is approximately 1.22 times the wavelength divided by the aperture diameter, thereby linking optical resolution directly to physical parameters.

Aperture Dependency

The diameter of a telescope’s aperture plays a crucial role in its resolving power. A larger aperture reduces the impact of diffraction, enabling smaller angular separations to be resolved, while a smaller aperture increases the diffraction effects, degrading resolution.

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