1. What is Angular Resolution?

Angular resolution is the ability of an optical instrument to distinguish small details of an object. It represents the smallest angle between two point sources that can be distinguished as separate entities.

2. How Does the Calculator Work?

The calculator uses the angular resolution formula:

Where:

• \( \theta \) — Angular resolution (radians)
• \( \lambda \) — Wavelength of light (meters)
• \( d \) — Diameter of the aperture (meters)
• 1.22 — Constant derived from the Rayleigh criterion

Explanation: The equation shows that resolution improves (smaller θ) with larger apertures and shorter wavelengths.

3. Importance of Angular Resolution

Details: Angular resolution is crucial in astronomy, microscopy, and imaging systems. It determines how fine details can be resolved in telescopes, cameras, and other optical instruments.

4. Using the Calculator

Tips: Enter wavelength and aperture diameter in meters. The calculator provides results in radians, degrees, and arcseconds for convenience.

5. Frequently Asked Questions (FAQ)

Q1: Why is there a factor of 1.22 in the formula?
A: The 1.22 factor comes from the Rayleigh criterion for circular apertures, accounting for the diffraction pattern of light.

Q2: What is a typical angular resolution for telescopes?
A: The Hubble Space Telescope has about 0.05 arcseconds resolution. Ground-based telescopes typically achieve 0.5-1 arcsecond due to atmospheric seeing.

Q3: How does wavelength affect resolution?
A: Shorter wavelengths (blue light) provide better resolution than longer wavelengths (red light) for the same aperture size.

Q4: Can angular resolution be better than the diffraction limit?
A: Under normal circumstances no, but techniques like interferometry can achieve better effective resolution by combining multiple telescopes.

Q5: How does this relate to human eye resolution?
A: The human eye has an angular resolution of about 1 arcminute (1/60 degree), limited by both the eye's aperture and retinal structure.