Understanding the Diffraction Limit
The diffraction limit is a fundamental constraint in optics that determines the finest detail an optical system can resolve. It arises from the wave nature of light and sets a theoretical limit on the resolving power of telescopes, microscopes, and other optical instruments.
The Formula (Rayleigh Criterion)
The diffraction limit is calculated using:
[\theta = 1.22 \times \frac{\lambda}{D}]
Where:
- ฮธ = Angular resolution in radians
- ฮป = Wavelength of light
- D = Diameter of the aperture
- 1.22 = Constant derived from the Bessel function for circular apertures
Example Calculation
For a telescope observing green light (550 nm) with a 0.25 m aperture:
[\theta = 1.22 \times \frac{550 \times 10^{-9}}{0.25}]
[\theta = 1.22 \times 2.2 \times 10^{-6}]
[\theta \approx 2.684 \times 10^{-6} \text{ radians}]
To convert to arc seconds, multiply by 206,265:
[\theta \approx 0.554 \text{ arc seconds}]
Applications
Astronomy
Telescope resolution is limited by diffraction. Larger telescopes can resolve finer details. The Hubble Space Telescope's 2.4 m mirror achieves about 0.05 arc seconds in visible light.
Microscopy
The diffraction limit determines the smallest features a microscope can resolve, typically 200-300 nm for optical microscopes.
Photography
Camera lens aperture affects image sharpness. Very small apertures (high f-numbers) can cause diffraction blur.
Factors Affecting Resolution
- Wavelength: Shorter wavelengths provide better resolution
- Aperture Diameter: Larger apertures improve resolution
- Atmospheric Effects: Ground-based telescopes are often limited by atmospheric turbulence