Numerical Aperture Calculator

Frequently Asked Questions

What does numerical aperture tell you?

Numerical aperture describes the cone of light a lens or fiber can accept or emit. A larger value means more light gathering and finer resolution.

How is numerical aperture related to f-number?

The f-number is approximately the reciprocal of twice the numerical aperture, so a small f-number corresponds to a large numerical aperture.

Why do microscope lenses use immersion oil?

Oil has a higher refractive index than air, which raises the numerical aperture above the limit set by air and improves resolution.

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How This Calculator Works

Numerical aperture describes the range of angles over which an optical system such as a lens, microscope objective, or optical fiber can accept or emit light. It is defined as the product of the refractive index of the medium in front of the lens and the sine of the acceptance half-angle measured from the optical axis. A larger numerical aperture means the system gathers light from a wider cone, which improves light-collecting power and resolving ability.

How To Use It

Enter the refractive index of the medium between the object and the lens. This is 1.0 for air, about 1.33 for water, and roughly 1.52 for immersion oil. Then enter the acceptance half-angle in degrees, which is half of the full cone angle. The calculator returns the numerical aperture and an equivalent f-number, a familiar way photographers describe the light-gathering speed of a lens.

Why It Matters

In microscopy a higher numerical aperture allows finer detail to be resolved because the diffraction-limited resolution improves as numerical aperture rises. Oil immersion objectives reach values above 1.0 precisely because oil raises the refractive index of the medium. In fiber optics the numerical aperture sets how easily light couples into the core.

Tips

Use the half-angle, not the full cone angle.

Immersion media raise numerical aperture above what air allows.

The f-number falls as numerical aperture rises.

Numerical Aperture Calculator

Frequently Asked Questions

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