Absorption Co-Efficient Calculator

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✖Degeneracy of Final State refers to the number of different quantum states with the same energy.ⓘ Degeneracy of Final State [g₂]			+10% -10%
✖Degeneracy of Initial State refers to the number of different quantum states with the same energy.ⓘ Degeneracy of Initial State [g₁]			+10% -10%
✖Density of Atoms Initial State represent the concentration of atoms in the respective energy levels.ⓘ Density of Atoms Initial State [N₁]			+10% -10%
✖Density of Atoms Final State represent the concentration of atoms in the respective energy levels.ⓘ Density of Atoms Final State [N₂]			+10% -10%
✖Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state.ⓘ Einstein Coefficient for Stimulated Absorption [B₂₁]			+10% -10%
✖Frequency of Transition represents the energy difference between the two states divided by Planck's constant.ⓘ Frequency of Transition [v₂₁]			+10% -10%
✖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 [n_ri]			+10% -10%

✖Absorption Coefficient represents the rate at which a material absorbs light. It is a measure of how strongly a material absorbs radiation per unit length.ⓘ Absorption Co-Efficient [α_a]

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Formula

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Absorption Co-Efficient

Formula

`"α"_{"a"} = "g"_{"2"}/"g"_{"1"}*("N"_{"1"}-"N"_{"2"})*("B"_{"21"}*"[hP]"*"v"_{"21"}*"n"_{"ri"})/"[c]"`

Example

`"9.7E^-41/m"="24"/"12"*("1.85electrons/m³"-"1.502electrons/m³")*("1.52m³"*"[hP]"*"41Hz"*"1.01")/"[c]"`

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Absorption Co-Efficient Solution

STEP 0: Pre-Calculation Summary

Formula Used

Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]
α_a = g₂/g₁*(N₁-N₂)*(B₂₁*[hP]*v₂₁*n_ri)/[c]
This formula uses 2 Constants, 8 Variables

Constants Used

[hP] - Planck constant Value Taken As 6.626070040E-34
[c] - Light speed in vacuum Value Taken As 299792458.0

Variables Used

Absorption Coefficient - (Measured in Diopter) - Absorption Coefficient represents the rate at which a material absorbs light. It is a measure of how strongly a material absorbs radiation per unit length.
Degeneracy of Final State - Degeneracy of Final State refers to the number of different quantum states with the same energy.
Degeneracy of Initial State - Degeneracy of Initial State refers to the number of different quantum states with the same energy.
Density of Atoms Initial State - (Measured in Electrons per Cubic Meter) - Density of Atoms Initial State represent the concentration of atoms in the respective energy levels.
Density of Atoms Final State - (Measured in Electrons per Cubic Meter) - Density of Atoms Final State represent the concentration of atoms in the respective energy levels.
Einstein Coefficient for Stimulated Absorption - (Measured in Cubic Meter) - Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state.
Frequency of Transition - (Measured in Hertz) - Frequency of Transition represents the energy difference between the two states divided by Planck's constant.
Refractive Index - 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.

STEP 1: Convert Input(s) to Base Unit

Degeneracy of Final State: 24 --> No Conversion Required
Degeneracy of Initial State: 12 --> No Conversion Required
Density of Atoms Initial State: 1.85 Electrons per Cubic Meter --> 1.85 Electrons per Cubic Meter No Conversion Required
Density of Atoms Final State: 1.502 Electrons per Cubic Meter --> 1.502 Electrons per Cubic Meter No Conversion Required
Einstein Coefficient for Stimulated Absorption: 1.52 Cubic Meter --> 1.52 Cubic Meter No Conversion Required
Frequency of Transition: 41 Hertz --> 41 Hertz No Conversion Required
Refractive Index: 1.01 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

α_a = g₂/g₁*(N₁-N₂)*(B₂₁*[hP]*v₂₁*n_ri)/[c] --> 24/12*(1.85-1.502)*(1.52*[hP]*41*1.01)/[c]

Evaluating ... ...

α_a = 9.68263090902183E-41

STEP 3: Convert Result to Output's Unit

9.68263090902183E-41 Diopter -->9.68263090902183E-41 1 per Meter (Check conversion here)

FINAL ANSWER

9.68263090902183E-41 ≈ 9.7E-41 1 per Meter <-- Absorption Coefficient

(Calculation completed in 00.004 seconds)

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< 12 Lasers Calculators

Small Signal Gain Coefficient

Go Signal Gain Coefficient = Density of Atoms Final State-(Degeneracy of Final State/Degeneracy of Initial State)*(Density of Atoms Initial State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]

Absorption Co-Efficient

Go Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]

Round Trip Gain

Go Round Trip Gain = Reflectances*Reflectances Separated by L*(exp(2*(Signal Gain Coefficient-Effective Loss Coefficient)*Length of Laser Cavity))

Transmittance

Go Transmittance = (sin(pi/Wavelength of Light*(Refractive Index)^3*Length of Fiber*Supply Voltage))^2

Ratio of Rate of Spontaneous and Stimulated Emission

Go Ratio of Rate of Spontaneous to Stimulus Emission = exp((([hP]*Frequency of Radiation)/([BoltZ]*Temperature))-1)

Irradiance

Go Irridance of Transmitted Beam = Irradiation of Light Incident*exp(Signal Gain Coefficient*Distance Travelled by Laser Beam)

Intensity of Signal at Distance

Go Intensity of Signal at Distance = Initial Intensity*exp(-Decay Constant*Distance of Measuring)

Variable Refractive Index of The GRIN Lens

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

Half Wave Voltage

Go Half Wave Voltage = Wavelength of Light/(Length of Fiber*Refractive Index^3)

Plane of Transmission of Analyzer

Go Plane of Transmission of Analyzer = Plane of Polarizer/((cos(Theta))^2)

Plane of Polarizer

Go Plane of Polarizer = Plane of Transmission of Analyzer*(cos(Theta)^2)

Single Pinhole

Go Single Pinhole = Wavelength of Wave/((Apex Angle*(180/pi))*2)

Absorption Co-Efficient Formula

How is the absorption coefficient formula relevant to lasers?

The formula is relevant to lasers as it provides insights into the factors influencing the absorption of light in a gain medium. Achieving and maintaining a population inversion is essential for laser amplification through stimulated emission, and the absorption coefficient is a key parameter in understanding this process.

How to Calculate Absorption Co-Efficient?

Absorption Co-Efficient calculator uses Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c] to calculate the Absorption Coefficient, The Absorption Co-Efficient formula is defined as the rate at which a material absorbs light. It is a measure of how strongly a material absorbs radiation per unit length. Absorption Coefficient is denoted by α_a symbol.

How to calculate Absorption Co-Efficient using this online calculator? To use this online calculator for Absorption Co-Efficient, enter Degeneracy of Final State (g₂), Degeneracy of Initial State (g₁), Density of Atoms Initial State (N₁), Density of Atoms Final State (N₂), Einstein Coefficient for Stimulated Absorption (B₂₁), Frequency of Transition (v₂₁) & Refractive Index (n_ri) and hit the calculate button. Here is how the Absorption Co-Efficient calculation can be explained with given input values -> 9.7E-41 = 24/12*(1.85-1.502)*(1.52*[hP]*41*1.01)/[c].

FAQ

What is Absorption Co-Efficient?

The Absorption Co-Efficient formula is defined as the rate at which a material absorbs light. It is a measure of how strongly a material absorbs radiation per unit length and is represented as α_a = g₂/g₁*(N₁-N₂)*(B₂₁*[hP]*v₂₁*n_ri)/[c] or Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]. Degeneracy of Final State refers to the number of different quantum states with the same energy, Degeneracy of Initial State refers to the number of different quantum states with the same energy, Density of Atoms Initial State represent the concentration of atoms in the respective energy levels, Density of Atoms Final State represent the concentration of atoms in the respective energy levels, Einstein Coefficient for Stimulated Absorption represents the probability per unit time for an atom in the lower energy state, Frequency of Transition represents the energy difference between the two states divided by Planck's constant & 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.

How to calculate Absorption Co-Efficient?

The Absorption Co-Efficient formula is defined as the rate at which a material absorbs light. It is a measure of how strongly a material absorbs radiation per unit length is calculated using Absorption Coefficient = Degeneracy of Final State/Degeneracy of Initial State*(Density of Atoms Initial State-Density of Atoms Final State)*(Einstein Coefficient for Stimulated Absorption*[hP]*Frequency of Transition*Refractive Index)/[c]. To calculate Absorption Co-Efficient, you need Degeneracy of Final State (g₂), Degeneracy of Initial State (g₁), Density of Atoms Initial State (N₁), Density of Atoms Final State (N₂), Einstein Coefficient for Stimulated Absorption (B₂₁), Frequency of Transition (v₂₁) & Refractive Index (n_ri). With our tool, you need to enter the respective value for Degeneracy of Final State, Degeneracy of Initial State, Density of Atoms Initial State, Density of Atoms Final State, Einstein Coefficient for Stimulated Absorption, Frequency of Transition & Refractive Index 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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