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Numerical Aperture Formula

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Numerical Aperture is a measure of the light-gathering or light-capturing ability of an optical fiber or an optical system. Check FAQs

NA = \sqrt{({η core}^{2}) - ({η clad}^{2})}

NA - Numerical Aperture?η_core - Refractive Index of Core?η_clad - Refractive Index of Cladding?

Numerical Aperture Example

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Here is how the Numerical Aperture equation looks like with Values.

Here is how the Numerical Aperture equation looks like with Units.

Here is how the Numerical Aperture equation looks like.

0.4021 = \sqrt{({1.335}^{2}) - ({1.273}^{2})}

0.4021 = \sqrt{({1.335}^{2}) - ({1.273}^{2})}

0.4021 = \sqrt{({1.335}^{2}) - ({1.273}^{2})}

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Numerical Aperture Solution

Follow our step by step solution on how to calculate Numerical Aperture?

FIRST Step Consider the formula

NA = \sqrt{({η core}^{2}) - ({η clad}^{2})}

Next Step Substitute values of Variables

∴

NA = \sqrt{({1.335}^{2}) - ({1.273}^{2})}

Next Step Prepare to Evaluate

∴

NA = \sqrt{({1.335}^{2}) - ({1.273}^{2})}

Next Step Evaluate

∴

NA = 0.40211441157959

LAST Step Rounding Answer

∴

NA = 0.4021

Numerical Aperture Formula Elements

Variables

Functions

Numerical Aperture

Numerical Aperture is a measure of the light-gathering or light-capturing ability of an optical fiber or an optical system.

Symbol: NA

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Numerical Aperture

Refractive Index of Core

The Refractive Index of Core is defined as how the light travels through that medium. It defines how much a light ray can bend when it enters from one medium to the other.

Symbol: η_core

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index of Core

Refractive Index of Cladding

Refractive Index of Cladding is the measure of bending of a ray of light when passing from one medium(surrounding) into another.

Symbol: η_clad

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Refractive Index of Cladding

sqrt

A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number.

Syntax: sqrt(Number)

Other formulas in Fiber Design Characteristics category

Go Refractive Index of Fiber Core

η core = \sqrt{{NA}^{2} + {η clad}^{2}}

Go Refractive Index of Cladding

η clad = \sqrt{{η core}^{2} - {NA}^{2}}

Go Ray Optics Critical Angle

θ = {\sin (\frac{η r}{η i})}^{- 1}

Go Normalized Frequency

V = \sqrt{2 \cdot N M}

How to Evaluate Numerical Aperture?

Numerical Aperture evaluator uses Numerical Aperture = sqrt((Refractive Index of Core^2)-(Refractive Index of Cladding^2)) to evaluate the Numerical Aperture, The Numerical Aperture formula is defined as the product of the refractive index of the beam from which the light input is received and the sine of the maximum ray angle against the axis, for which light can be transmitted through the system based on purely geometric considerations. Numerical Aperture is denoted by NA symbol.

How to evaluate Numerical Aperture using this online evaluator? To use this online evaluator for Numerical Aperture, enter Refractive Index of Core (η_core) & Refractive Index of Cladding (η_clad) and hit the calculate button.

FAQs on Numerical Aperture

What is the formula to find Numerical Aperture?

The formula of Numerical Aperture is expressed as Numerical Aperture = sqrt((Refractive Index of Core^2)-(Refractive Index of Cladding^2)). Here is an example- 0.402114 = sqrt((1.335^2)-(1.273^2)).

How to calculate Numerical Aperture?

With Refractive Index of Core (η_core) & Refractive Index of Cladding (η_clad) we can find Numerical Aperture using the formula - Numerical Aperture = sqrt((Refractive Index of Core^2)-(Refractive Index of Cladding^2)). This formula also uses Square Root Function function(s).

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Numerical Aperture Formula

Numerical Aperture Example

Numerical Aperture Solution

Numerical Aperture Formula Elements

Other formulas in Fiber Design Characteristics category

How to Evaluate Numerical Aperture?

FAQs on Numerical Aperture

Variable Name