Numerical Aperture (NA) Calculator
Calculate the light-gathering capability and resolution limit of your optical system.
What is Numerical Aperture?
Numerical Aperture (NA) is a dimensionless number that characterizes the range of angles over which an optical system can accept or emit light. In microscopy, NA is critical because it determines the resolving power of an objective lens. The higher the NA, the better the specimen detail and the brighter the image.
Where:
- n is the refractive index of the medium in which the lens is working (e.g., air, water, or oil).
- θ is the maximal half-angle of the cone of light that can enter or exit the lens.
How to Calculate NA
To use the calculator, follow these steps:
- Enter the Refractive Index: If you are using a standard "dry" objective, the value is 1.0. For water immersion, use 1.33, and for common immersion oils, use approximately 1.51 to 1.52.
- Enter the Half-Angle: This is the angle from the optical axis to the outermost ray accepted by the lens. Note that the full cone angle is 2θ.
- (Optional) Wavelength: Enter the light wavelength to calculate the theoretical Abbe resolution limit.
Theoretical Resolution Limit
According to Ernst Abbe, the lateral resolution (d) is limited by the wavelength of light and the numerical aperture. The formula used in this calculator is:
A smaller value for 'd' indicates higher resolution (the ability to distinguish two points that are very close together).
Practical Example
Suppose you have an oil immersion lens (n = 1.515) with a light-gathering half-angle of 60 degrees. Using the formula:
- NA = 1.515 × sin(60°)
- NA = 1.515 × 0.866
- NA = 1.31
If using green light (550nm), the resolution would be approximately 550 / (2 × 1.31) = 210 nm.