Variable Refractive Index of The GRIN Lens Calculator

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✖Refractive Index of Medium 1 is the ratio of speed of light in vacuum to speed of light in medium 1.ⓘ Refractive Index of Medium 1 [n₁]			+10% -10%
✖Positive Constant is a number greater than zero that does not change with time.ⓘ Positive Constant [A_con]			+10% -10%
✖Radius of Lens is defined as the distance between the centre of curvature of the lens and the edge of the lens.ⓘ Radius of Lens [R_lens]			+10% -10%

✖Apparent Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.ⓘ Variable Refractive Index of The GRIN Lens [n_r]

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Formula

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Variable Refractive Index of The GRIN Lens

Formula

`"n"_{"r"} = "n"_{"1"}*(1-("A"_{"con"}*"R"_{"lens"}^2)/2)`

Example

`"1.453125"="1.5"*(1-("10000"*("0.0025m")^2)/2)`

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Variable Refractive Index of The GRIN Lens Solution

STEP 0: Pre-Calculation Summary

Formula Used

Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2)
n_r = n₁*(1-(A_con*R_lens^2)/2)
This formula uses 4 Variables

Variables Used

Apparent Refractive Index - Apparent Refractive Index is a dimensionless quantity that describes how much light is slowed down or refracted when entering a medium compared to its speed in a vacuum.
Refractive Index of Medium 1 - Refractive Index of Medium 1 is the ratio of speed of light in vacuum to speed of light in medium 1.
Positive Constant - Positive Constant is a number greater than zero that does not change with time.
Radius of Lens - (Measured in Meter) - Radius of Lens is defined as the distance between the centre of curvature of the lens and the edge of the lens.

STEP 1: Convert Input(s) to Base Unit

Refractive Index of Medium 1: 1.5 --> No Conversion Required
Positive Constant: 10000 --> No Conversion Required
Radius of Lens: 0.0025 Meter --> 0.0025 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n_r = n₁*(1-(A_con*R_lens^2)/2) --> 1.5*(1-(10000*0.0025^2)/2)

Evaluating ... ...

n_r = 1.453125

STEP 3: Convert Result to Output's Unit

1.453125 --> No Conversion Required

FINAL ANSWER

1.453125 <-- Apparent Refractive Index

(Calculation completed in 00.004 seconds)

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Created by Priyanka G Chalikar

The National Institute Of Engineering (NIE), Mysuru

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Dayananda Sagar College Of Engineering (DSCE), Banglore

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< 12 Lasers Calculators

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Variable Refractive Index of The GRIN Lens

Go Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2)

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Variable Refractive Index of The GRIN Lens Formula

Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2)
n_r = n₁*(1-(A_con*R_lens^2)/2)

What is the significance of variable refractive index?

When refractive index varies in a controlled way, the combining of the refraction which occurs at the surface of the lens with that an image can be produced that is immune to aberrations that are non-idealities of lenses.

How to Calculate Variable Refractive Index of The GRIN Lens?

Variable Refractive Index of The GRIN Lens calculator uses Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2) to calculate the Apparent Refractive Index, Variable Refractive Index of The GRIN Lens (Gradient Index) formula is defined as the refractive index of the cylindrical lens that varies with the radius of the lens. Here, RI is the refractive index on the lens axis, and A is a positive constant. Apparent Refractive Index is denoted by n_r symbol.

How to calculate Variable Refractive Index of The GRIN Lens using this online calculator? To use this online calculator for Variable Refractive Index of The GRIN Lens, enter Refractive Index of Medium 1 (n₁), Positive Constant (A_con) & Radius of Lens (R_lens) and hit the calculate button. Here is how the Variable Refractive Index of The GRIN Lens calculation can be explained with given input values -> 1.453125 = 1.5*(1-(10000*0.0025^2)/2).

FAQ

What is Variable Refractive Index of The GRIN Lens?

Variable Refractive Index of The GRIN Lens (Gradient Index) formula is defined as the refractive index of the cylindrical lens that varies with the radius of the lens. Here, RI is the refractive index on the lens axis, and A is a positive constant and is represented as n_r = n₁*(1-(A_con*R_lens^2)/2) or Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2). Refractive Index of Medium 1 is the ratio of speed of light in vacuum to speed of light in medium 1, Positive Constant is a number greater than zero that does not change with time & Radius of Lens is defined as the distance between the centre of curvature of the lens and the edge of the lens.

How to calculate Variable Refractive Index of The GRIN Lens?

Variable Refractive Index of The GRIN Lens (Gradient Index) formula is defined as the refractive index of the cylindrical lens that varies with the radius of the lens. Here, RI is the refractive index on the lens axis, and A is a positive constant is calculated using Apparent Refractive Index = Refractive Index of Medium 1*(1-(Positive Constant*Radius of Lens^2)/2). To calculate Variable Refractive Index of The GRIN Lens, you need Refractive Index of Medium 1 (n₁), Positive Constant (A_con) & Radius of Lens (R_lens). With our tool, you need to enter the respective value for Refractive Index of Medium 1, Positive Constant & Radius of 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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