Luneburg Lens Refractive Index Calculator

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Radar Antennas Reception

Radar & Antenna Specifications

Special Purpose Radars

✖Radial Distance is the measurement of the distance from the center of the Luneburg Lens to any point of interest.ⓘ Radial Distance [r]			+10% -10%
✖Radius of Luneburg Lens is the measurement of the distance from the centre to the circumference of the lens.ⓘ Radius of Luneburg Lens [r_o]			+10% -10%

✖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.ⓘ Luneburg Lens Refractive Index [η_l]

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Formula

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Luneburg Lens Refractive Index

Formula

`"η"_{"l"} = sqrt(2-("r"/"r"_{"o"})^2)`

Example

`"1.382447"=sqrt(2-("1.69m"/"5.67m")^2)`

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Luneburg Lens Refractive Index Solution

STEP 0: Pre-Calculation Summary

Formula Used

Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2)
η_l = sqrt(2-(r/r_o)^2)
This formula uses 1 Functions, 3 Variables

Functions Used

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., sqrt(Number)

Variables Used

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.
Radial Distance - (Measured in Meter) - Radial Distance is the measurement of the distance from the center of the Luneburg Lens to any point of interest.
Radius of Luneburg Lens - (Measured in Meter) - Radius of Luneburg Lens is the measurement of the distance from the centre to the circumference of the lens.

STEP 1: Convert Input(s) to Base Unit

Radial Distance: 1.69 Meter --> 1.69 Meter No Conversion Required
Radius of Luneburg Lens: 5.67 Meter --> 5.67 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

η_l = sqrt(2-(r/r_o)^2) --> sqrt(2-(1.69/5.67)^2)

Evaluating ... ...

η_l = 1.38244719878452

STEP 3: Convert Result to Output's Unit

1.38244719878452 --> No Conversion Required

FINAL ANSWER

1.38244719878452 ≈ 1.382447 <-- Luneburg Lens Refractive Index

(Calculation completed in 00.004 seconds)

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Credits

Created by Santhosh Yadav

Dayananda Sagar College Of Engineering (DSCE), Banglore

Santhosh Yadav has created this Calculator and 50+ more calculators!

Verified by Ritwik Tripathi

Vellore Institute of Technology (VIT Vellore), Vellore

Ritwik Tripathi has verified this Calculator and 100+ more calculators!

< 14 Radar Antennas Reception Calculators

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Go Omnidirectional SIR = 1/(2*(Frequency Reuse Ratio-1)^(-Propagation Path Loss Exponent)+2*(Frequency Reuse Ratio)^(-Propagation Path Loss Exponent)+2*(Frequency Reuse Ratio+1)^(-Propagation Path Loss Exponent))

Dielectric Constant of Artificial Dielectric

Go Dielectric Constant of Artificial Dielectric = 1+(4*pi*Radius of Metallic Spheres^3)/(Spacing between Centers of Metallic Sphere^3)

Maximum Gain of Antenna given Antenna Diameter

Go Maximum Gain of Antenna = (Antenna Aperture Efficiency/43)*(Antenna Diameter/Dielectric Constant of Artificial Dielectric)^2

Metal-Plate Lens Refractive Index

Go Metal Plate Refractive Index = sqrt(1-(Incident Wave Wavelength/(2*Spacing between Centers of Metallic Sphere))^2)

Spacing between Centers of Metallic Sphere

Go Spacing between Centers of Metallic Sphere = Incident Wave Wavelength/(2*sqrt(1-Metal Plate Refractive Index^2))

Overall Noise Figure of Cascaded Networks

Go Overall Noise Figure = Noise Figure Network 1+(Noise Figure Network 2-1)/Gain of Network 1

Receiver Antenna Gain

Go Receiver Antenna Gain = (4*pi*Effective Area of Receiving Antenna)/Carrier Wavelength^2

Luneburg Lens Refractive Index

Go Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2)

Likelihood Ratio Receiver

Go Likelihood Ratio Receiver = Probability Density Function of Signal and Noise/Probability Density Function of Noise

Frequency Reuse Ratio

Go Frequency Reuse Ratio = (6*Signal to Co-channel Interference Ratio)^(1/Propagation Path Loss Exponent)

Directive Gain

Go Directive Gain = (4*pi)/(Beam Width in X-plane*Beam Width in Y-plane)

Signal to Co-channel Interference Ratio

Go Signal to Co-channel Interference Ratio = (1/6)*Frequency Reuse Ratio^Propagation Path Loss Exponent

Effective Aperture of Lossless Antenna

Go Effective Aperture of Lossless Antenna = Antenna Aperture Efficiency*Physical Area of an Antenna

Effective Noise Temperature

Go Effective Noise Temperature = (Overall Noise Figure-1)*Noise Temperature Network 1

Luneburg Lens Refractive Index Formula

Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2)
η_l = sqrt(2-(r/r_o)^2)

How is Luneburg Lens Refractive Index different from normal lens refractive index?

Luneburg Lenses have a gradient refractive index, meaning that the refractive index varies with radial distance from the center of the lens. This variation allows for unique optical and electromagnetic properties within the lens. In contrast, traditional lenses have a constant refractive index, typically greater than 1, which causes light to bend as it enters the lens.

How to Calculate Luneburg Lens Refractive Index?

Luneburg Lens Refractive Index calculator uses Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2) to calculate 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 calculate Luneburg Lens Refractive Index using this online calculator? To use this online calculator for Luneburg Lens Refractive Index, enter Radial Distance (r) & Radius of Luneburg Lens (r_o) and hit the calculate button. Here is how the Luneburg Lens Refractive Index calculation can be explained with given input values -> 1.382447 = sqrt(2-(1.69/5.67)^2).

FAQ

What is 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 and is represented as η_l = sqrt(2-(r/r_o)^2) or Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2). Radial Distance is the measurement of the distance from the center of the Luneburg Lens to any point of interest & Radius of Luneburg Lens is the measurement of the distance from the centre to the circumference of the lens.

How to calculate 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 is calculated using Luneburg Lens Refractive Index = sqrt(2-(Radial Distance/Radius of Luneburg Lens)^2). To calculate Luneburg Lens Refractive Index, you need Radial Distance (r) & Radius of Luneburg Lens (r_o). With our tool, you need to enter the respective value for Radial Distance & Radius of Luneburg Lens and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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