# Can numerical aperture be less than 1?

## Can Numerical Aperture Be Less Than 1?

Yes, the numerical aperture (NA) of an optical system can indeed be less than 1. The numerical aperture is a dimensionless number that characterizes the range of angles over which the system can accept or emit light. It is defined as:

NA = n * sin(θ)

where n is the refractive index of the medium in which the lens or optical system is working (for air, n is typically 1), and θ is the half-angle of the maximum cone of light that can enter or exit the lens or optical system.

For optical systems in air (n=1), the maximum possible value of NA is 1, which corresponds to a half-angle of 90°, meaning the system can capture light coming from all directions in the plane perpendicular to the lens axis. However, in practice, most optical systems have a numerical aperture less than 1 because it is challenging to design and manufacture lenses that can capture light at such extreme angles with high efficiency and without significant aberrations.

Furthermore, when an optical system operates in a medium with a refractive index greater than 1, such as water or glass, the NA can exceed 1. This is because the sine function in the NA formula can effectively be 'multiplied' by the refractive index of the medium, allowing for a higher NA. However, when operating in air or vacuum, the refractive index is approximately 1, and thus, the NA is typically less than 1.

In summary, the numerical aperture being less than 1 is common for many optical systems, especially those designed to operate in air or similar environments. This limitation is primarily due to practical constraints in lens design and the inherent properties of light propagation.