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)
ηl = sqrt(2-(r/ro)^2)
This formula uses 1 Functions, 3 Variables
Functions Used
sqrt - Square root function, 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
ηl = sqrt(2-(r/ro)^2) --> sqrt(2-(1.69/5.67)^2)
Evaluating ... ...
ηl = 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)

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

Omnidirectional SIR
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)
ηl = sqrt(2-(r/ro)^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 ηl 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 (ro) 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 ηl = sqrt(2-(r/ro)^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 (ro). 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.
Let Others Know
Facebook
Twitter
Reddit
LinkedIn
Email
WhatsApp
Copied!