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Luneburg Lens Refractive Index Formula

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Luneburg Lens Refractive Index describes how much light or other electromagnetic waves slow down or change their speed when they pass through that material compared to their speed in a vacuum. Check FAQs

η l = \sqrt{2 - {(\frac{r}{r o})}^{2}}

η_l - Luneburg Lens Refractive Index?r - Radial Distance?r_o - Radius of Luneburg Lens?

Luneburg Lens Refractive Index Example

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Here is how the Luneburg Lens Refractive Index equation looks like with Values.

Here is how the Luneburg Lens Refractive Index equation looks like with Units.

Here is how the Luneburg Lens Refractive Index equation looks like.

1.3824 = \sqrt{2 - {(\frac{1.69}{5.67})}^{2}}

1.3824 = \sqrt{2 - {(\frac{1.69m}{5.67m})}^{2}}

1.3824 = \sqrt{2 - {(\frac{1.69}{5.67})}^{2}}

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Luneburg Lens Refractive Index Solution

Follow our step by step solution on how to calculate Luneburg Lens Refractive Index?

FIRST Step Consider the formula

η l = \sqrt{2 - {(\frac{r}{r o})}^{2}}

Next Step Substitute values of Variables

∴

η l = \sqrt{2 - {(\frac{1.69m}{5.67m})}^{2}}

Next Step Prepare to Evaluate

∴

η l = \sqrt{2 - {(\frac{1.69}{5.67})}^{2}}

Next Step Evaluate

∴

η l = 1.38244719878452

LAST Step Rounding Answer

∴

η l = 1.3824

Luneburg Lens Refractive Index Formula Elements

Variables

Functions

Luneburg Lens Refractive Index

Luneburg Lens Refractive Index describes how much light or other electromagnetic waves slow down or change their speed when they pass through that material compared to their speed in a vacuum.

Symbol: η_l

Measurement: NAUnit: Unitless

Note: Value should be greater than 0.

Formulas to find Luneburg Lens Refractive Index

Radial Distance

Radial Distance is the measurement of the distance from the center of the Luneburg Lens to any point of interest.

Symbol: r

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radial Distance

Radius of Luneburg Lens

Radius of Luneburg Lens is the measurement of the distance from the centre to the circumference of the lens.

Symbol: r_o

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Radius of Luneburg Lens

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 Radar Antennas Reception category

Go Directive Gain

G d = \frac{4 \cdot π}{θ b \cdot φ b}

Go Spacing between Centers of Metallic Sphere

s = \frac{λ m}{2 \cdot \sqrt{1 - {η m}^{2}}}

Go Effective Aperture of Lossless Antenna

A e = η a \cdot A

Go Dielectric Constant of Artificial Dielectric

e = 1 + \frac{4 \cdot π \cdot a^{3}}{s^{3}}

How to Evaluate Luneburg Lens Refractive Index?

Luneburg Lens Refractive Index evaluator uses Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2) to evaluate the Luneburg Lens Refractive Index, Luneburg Lens Refractive Index is the gradient refractive index which means it varies with radial distance from the center of the lens. The refractive index is highest at the center of the lens (r=0) and decreases as you move toward the outer edge of the lens. Luneburg Lens Refractive Index is denoted by η_l symbol.

How to evaluate Luneburg Lens Refractive Index using this online evaluator? To use this online evaluator for Luneburg Lens Refractive Index, enter Radial Distance (r) & Radius of Luneburg Lens (r_o) and hit the calculate button.

FAQs on Luneburg Lens Refractive Index

What is the formula to find Luneburg Lens Refractive Index?

The formula of Luneburg Lens Refractive Index is expressed as Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2). Here is an example- 1.382447 = sqrt(2-(1.69/5.67)^2).

How to calculate Luneburg Lens Refractive Index?

With Radial Distance (r) & Radius of Luneburg Lens (r_o) we can find Luneburg Lens Refractive Index using the formula - Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2). This formula also uses Square Root (sqrt) function(s).

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Luneburg Lens Refractive Index Formula

Luneburg Lens Refractive Index Example

Luneburg Lens Refractive Index Solution

Luneburg Lens Refractive Index Formula Elements

Other formulas in Radar Antennas Reception category

How to Evaluate Luneburg Lens Refractive Index?

FAQs on Luneburg Lens Refractive Index

Variable Name