Table of Contents
Numerical aperture (NA) is a key parameter in optics that influences the resolving power of lenses and microscopes. It determines the ability of a lens to gather light and resolve fine details in an image. Understanding how to calculate NA and its effect on optical resolution is essential for designing and using optical systems effectively.
What is Numerical Aperture?
Numerical aperture is a dimensionless number that characterizes the range of angles over which a system can collect light. It is defined as the product of the refractive index of the medium and the sine of the half-angle of the maximum light cone captured by the lens.
Calculating Numerical Aperture
The formula for calculating NA is:
NA = n × sin(θ)
Where n is the refractive index of the medium between the lens and the object, and θ is the half-angle of the light cone entering the lens. For example, in air (n ≈ 1.0), if the maximum angle θ is 30°, then NA = 1.0 × sin(30°) = 0.5.
Impact on Optical Resolution
Higher NA values allow lenses to gather more light and resolve finer details. The resolution limit of an optical system can be approximated by the Rayleigh criterion:
Resolution ≈ 0.61 λ / NA
Where λ is the wavelength of light used. Increasing the NA decreases the minimum resolvable distance, improving the system’s ability to distinguish between close objects.
Summary
- Numerical aperture measures light-gathering ability.
- Calculated as NA = n × sin(θ).
- Higher NA improves resolution and image clarity.
- Resolution depends inversely on NA.