Numerical Aperture Calculator

Numerical Aperture Calculator | Online Free Tool | Elysia Tools

Tool usage guide

Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Category: Science & Education
Input types: number
Output type: text
Sample coverage: 4
API ready: Yes

Overview

Calculate the numerical aperture (NA) of microscope objectives and optical systems using medium refractive index and acceptance angle. The tool computes the total acceptance cone, numerical aperture via NA = n·sinα, and the diffraction-limited Abbe resolution limit for any specified illumination wavelength.

When to use

Determining light gathering capacity and lateral resolution limits for dry or immersion microscope objectives.
Evaluating light coupling acceptance cones and numerical aperture for optical fibers and condenser lenses.
Comparing diffraction-limited resolving power across different immersion media like air, water, and immersion oil.

How it works

1Enter the refractive index (n) of the medium between the objective lens and sample.
2Specify the half acceptance angle (α) in degrees to calculate the light collection cone and numerical aperture (NA = n·sinα).
3Optionally provide the illumination wavelength (λ) in nanometers to compute the theoretical Abbe diffraction resolution limit (d = λ / (2·NA)).

Use cases

Microscopy objective selection: Evaluating whether a dry, water, or oil immersion lens meets the required resolution threshold.
Optical fiber acceptance angle analysis: Computing numerical aperture and half-angle boundaries for efficient light coupling.
Fluorescence microscopy planning: Calculating diffraction-limited spot sizes for specific fluorophore emission wavelengths.

Examples

1. Dry Objective Resolution Analysis

Microscopy Lab Technician

Background

Evaluating a standard 40x air objective for imaging mammalian cells at 550 nm illumination.

Problem

Determine the exact NA and diffraction resolution limit for an air lens with a 30° half-acceptance angle.

How to use

Set refractive index to 1.0, half acceptance angle to 30°, and wavelength to 550 nm.

refractiveIndex: 1.0, halfAngleDeg: 30, wavelengthNm: 550

Outcome

Calculates an NA of 0.500000, a 60° full acceptance cone, and an Abbe resolution limit of 550.00 nm.

2. Oil Immersion Objective Optimization

Optical Systems Engineer

Background

Designing a high-resolution 100x immersion lens system to image sub-cellular bacterial features.

Problem

Find the resolving power gain when using immersion oil (n = 1.515) with a 60° acceptance half-angle.

How to use

Set refractive index to 1.515, half acceptance angle to 60°, and wavelength to 550 nm.

FAQ

What is numerical aperture (NA)?

Numerical aperture is a dimensionless measure of an optical system's ability to gather light and resolve fine specimen detail, defined as NA = n·sinα.

Why can a dry objective not exceed an NA of 1.0?

In air (n ≈ 1.0), sinα reaches a maximum theoretical value of 1 at 90°, making an NA greater than 1.0 physically impossible without immersion media.

How does immersion oil improve optical resolution?

Immersion oil has a refractive index close to glass (n ≈ 1.515), preventing light refraction at the coverslip and enabling higher acceptance angles and higher NA values.

How is the Abbe resolution limit calculated?

The lateral Abbe resolution limit is calculated using the formula d = λ / (2·NA), where λ is the light wavelength and NA is the numerical aperture.

Is the wavelength field mandatory?

No, wavelength is optional and is only required if you want to calculate the Abbe diffraction resolution limit alongside the NA.

refractiveIndex: 1.515, halfAngleDeg: 60, wavelengthNm: 550

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Learn when to use this tool, what it supports, and how real users apply it.

Key facts

Overview

When to use

How it works

Use cases

Examples

1. Dry Objective Resolution Analysis

2. Oil Immersion Objective Optimization

FAQ

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