Physics
Physics
Problem
A telescope must resolve two stars separated by when observing light of wavelength . Determine the minimum diameter of its objective that will meet this requirement.Intuitive explanation
The key here is diffraction-limited resolution: a telescope's ability to distinguish two nearby objects depends on how much its aperture spreads out light waves. The Rayleigh criterion gives you the minimum angular separation a telescope can resolve, and it depends on both wavelength and aperture diameter. Longer wavelengths and smaller telescopes blur objects together more, so you'll need to rearrange the criterion to find the diameter required for your specific angular separation and wavelength.
Intuitive explanation
The key here is diffraction-limited resolution: a telescope's ability to distinguish two nearby objects depends on how much its aperture spreads out light waves. The Rayleigh criterion gives you the minimum angular separation a telescope can resolve, and it depends on both wavelength and aperture diameter. Longer wavelengths and smaller telescopes blur objects together more, so you'll need to rearrange the criterion to find the diameter required for your specific angular separation and wavelength.