1. What is Numerical Aperture?

Numerical Aperture (NA) is a dimensionless number that characterizes the range of angles over which a microscope can accept or emit light. It determines the resolving power and light gathering ability of the optical system.

2. How Does the Calculator Work?

The calculator uses the Numerical Aperture formula:

Where:

• \( n \) — Refractive index of the medium between the lens and specimen (unitless)
• \( \theta \) — Half-angle of the maximum cone of light that can enter or exit the lens (radians)

Explanation: The NA increases with both the refractive index of the medium and the angular aperture of the lens.

3. Importance of Numerical Aperture

Details: Higher NA values provide better resolution and brighter images. NA determines the microscope's ability to gather light and resolve fine specimen detail.

4. Using the Calculator

Tips: Enter refractive index (typically 1.0 for air, 1.33 for water, 1.51 for oil) and half-angle in radians (π/2 ≈ 1.5708 is maximum possible angle).

5. Frequently Asked Questions (FAQ)

Q1: What are typical NA values for microscope objectives?
A: Dry objectives: 0.1-0.95, Water immersion: up to 1.2, Oil immersion: up to 1.45-1.6.

Q2: How does NA affect resolution?
A: Resolution = λ/(2NA), where λ is wavelength. Higher NA means better resolution.

Q3: Why is oil used in high-NA microscopy?
A: Immersion oil has higher refractive index than air, allowing for greater light collection angles.

Q4: What's the relationship between NA and magnification?
A: While related, NA is more fundamental as it determines resolution. Magnification without sufficient NA results in empty magnification.

Q5: Can NA be greater than 1?
A: Yes, with immersion fluids having refractive index >1 and angles approaching 90° (sin(90°)=1).