Luneburg Lens Refractive Index Solution

STEP 0: Pre-Calculation Summary
Formula Used
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
1.38244719878452 1.382447 <-- Luneburg Lens Refractive Index
(Calculation completed in 00.004 seconds)
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Luneburg Lens Refractive Index Formula

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.
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