What is Numerical Aperture and Why it is Important?

What is the Numerical aperture in a microscope?

The numerical aperture (NA) of an optical system is a dimensionless number that characterizes the range of angles over which the system can accept or emit light.

By incorporating the index of refraction in its definition, NA has the property that it is constant for a beam as it goes from one material to another, provided there is no refractive power at the interface.

The exact definition of the term varies slightly between different areas of optics. Numerical aperture is commonly used in microscopy to describe the acceptance cone of an objective (and hence its light-gathering ability and resolution), and in fiber optics, in which it describes the range of angles within which light that is incident on the fiber will be transmitted along with it.

Numerical Aperture (also termed Object-Side Aperture) is a value (often symbolized by the abbreviation NA) originally defined by Abbe for microscope objectives and condensers. It is given by the simple expression:

Numerical Aperture (NA)=n×sin(µ) or n×sin(α)

Note: Many authors use the variable µ to designate the one-half angular aperture while others employ the more common term α, and in some instances, θ.

In the numerical aperture equation, n represents the refractive index of the medium between the objective front lens and the specimen, and µ or α is the one-half angular aperture of the objective.

The numerical aperture of a microscope objective is a measure of its ability to gather light and resolve fine specimen detail at a fixed object distance.

Image-forming light waves pass through the specimen and enter the objective in an inverted cone. A longitudinal slice of this cone of light reveals the angular aperture, a value that is determined by the focal length of the objective.

In practice, it is difficult to achieve numerical aperture values above 0.95 with dry objectives. As the light cones grow larger, the angular aperture (α) increases from 7° to 60°, with a resulting increase in the numerical aperture from 0.12 to 0.87, nearing the limit when air is utilized as the imaging medium.

Higher numerical apertures can be obtained by increasing the imaging medium refractive index (n) between the specimen and the objective front lens.

Microscope objectives are now available that allow imaging in alternative media such as water (refractive index = 1.33), glycerin (refractive index = 1.47), and immersion oil (refractive index = 1.51). The numerical aperture of an objective is also dependent, to a certain degree, upon the amount of correction for optical aberration.

numerical aperture

Why you should care about the numerical aperture?

So, why should you care about the numerical aperture of a lens anyway? When you are planning your experiment, you probably think about what magnification you are going to use, after all, you need to be able to see the structure you are interested in

Magnification is nothing, however, without enough resolution to distinguish your structure of interest from everything else in the sample.

How oil and water affect the numerical aperture

What does this have to do with water and oil immersion lenses? When light leaves your sample and enters the air (or water or oil) it refracts. Refraction simply means that the angle of light changes by some degrees- it changes direction slightly. When you use a water or oil immersion lens, you change how much the light refracts when it leaves the sample. This increases the theoretical limit of the numerical aperture of your lens. How much does it change it?


  • where NA = numerical aperture
  • n = index of refraction of the medium (eg. air, water, oil, etc.)
  • α= the half-angle of the cone of light that can enter the lens.

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