Numerical Aperture Calculator

Formula

To calculate the numerical aperture:

\[ NA = n \times \sin(\theta) \]

Where:

\(NA\) is the Numerical Aperture
\(n\) is the Index of Refraction
\(\theta\) is the Maximum Half-Angle of the cone of light that enters or exits the lens

What is Numerical Aperture?

A numerical aperture is defined as a unit-less and dimensionless number that describes the range of angles that a lens can emit or accept light. It is a crucial concept in optics, particularly in microscopy and fiber optics, as it determines the resolving power and light-gathering ability of a lens.

Example Calculation 1

Let's assume the following values:

Index of Refraction (\(n\)) = 1.5
Maximum Half-Angle (\(\theta\)) = 30 degrees

Using the formula:

\[ NA = 1.5 \times \sin(30^\circ) = 1.5 \times 0.5 = 0.75 \]

The Numerical Aperture is 0.75.

Example Calculation 2

Let's assume the following values:

Index of Refraction (\(n\)) = 1.33
Maximum Half-Angle (\(\theta\)) = 45 degrees

Using the formula:

\[ NA = 1.33 \times \sin(45^\circ) = 1.33 \times 0.707 = 0.94 \]

The Numerical Aperture is 0.94.