1. What is the Abbe Diffraction Limit?

The Abbe diffraction limit, formulated by Ernst Abbe in 1873, defines the maximum resolution achievable by an optical microscope. It represents the smallest distance between two points that can be distinguished as separate entities.

2. How Does the Calculator Work?

The calculator uses the Abbe diffraction limit formula:

Where:

• \( d \) — Resolution limit (micrometers)
• \( \lambda \) — Wavelength of light (nanometers)
• \( NA \) — Numerical aperture (unitless)
• 0.61 — Constant derived from diffraction theory

Explanation: The formula shows that resolution improves with shorter wavelengths and higher numerical apertures. The constant 0.61 comes from the Rayleigh criterion for circular apertures.

3. Importance of Resolution Limit Calculation

Details: Understanding the resolution limit is crucial for selecting appropriate microscopy techniques, designing optical systems, and interpreting microscopic images accurately.

4. Using the Calculator

Tips: Enter wavelength in nanometers (typical visible light: 400-700 nm) and numerical aperture (typically 0.1-1.4 for air and oil immersion objectives). Both values must be positive.

5. Frequently Asked Questions (FAQ)

Q1: What is numerical aperture (NA)?
A: Numerical aperture is a measure of the light-gathering ability of an optical system, defined as NA = n × sin(θ), where n is the refractive index and θ is the half-angle of the maximum cone of light.

Q2: Can resolution be better than the Abbe limit?
A: Conventional optical microscopy cannot surpass the Abbe limit, but super-resolution techniques like STED, PALM, and STORM can achieve higher resolution.

Q3: How does immersion oil improve resolution?
A: Immersion oil has a higher refractive index (n≈1.5) than air (n=1.0), allowing for higher numerical apertures and thus better resolution.

Q4: What is the typical resolution of a light microscope?
A: For visible light (λ=550 nm) and high NA objective (NA=1.4), the resolution limit is approximately 0.24 micrometers.

Q5: How does wavelength affect resolution?
A: Shorter wavelengths (blue/violet light) provide better resolution than longer wavelengths (red light) due to the inverse relationship in the formula.