Essen and Froome Formula for Group Refractive Index Calculator

✖Barometric Pressure is the pressure on earth that is caused by the weight of the air above us. It is sometimes the atmospheric pressure. It should be entered in millibar.ⓘ Barometric Pressure [P_b]			+10% -10%
✖Temperature in Celsius is the degree of coolness or hotness of any substance. It should be entered in degree celsius.ⓘ Temperature in Celsius [t]			+10% -10%
✖Partial pressure of water vapour is the vapour pressure in any gas mixture in equilibrium with solid or liquid water.ⓘ Partial Pressure of Water Vapour [e]			+10% -10%

✖Group Refractive Index is the he ratio of the vacuum velocity of light to the group velocity in a medium.ⓘ Essen and Froome Formula for Group Refractive Index [n]

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Formula

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Essen and Froome Formula for Group Refractive Index

Formula

`"n" = 1+(77.624*"P"_{"b"}*10^-6/(273.15+"t"))+((0.372/(273.15+"t")^2)-(12.92*10^-6/(273.15+"t")))*"e"`

Example

`"1.269616"=1+(77.624*"6921.213"*10^-6/(273.15+"98"))+((0.372/(273.15+"98")^2)-(12.92*10^-6/(273.15+"98")))*"1006mbar"`

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Essen and Froome Formula for Group Refractive Index Solution

STEP 0: Pre-Calculation Summary

Formula Used

Group Refractive Index = 1+(77.624*Barometric Pressure*10^-6/(273.15+Temperature in Celsius))+((0.372/(273.15+Temperature in Celsius)^2)-(12.92*10^-6/(273.15+Temperature in Celsius)))*Partial Pressure of Water Vapour
n = 1+(77.624*P_b*10^-6/(273.15+t))+((0.372/(273.15+t)^2)-(12.92*10^-6/(273.15+t)))*e
This formula uses 4 Variables

Variables Used

Group Refractive Index - Group Refractive Index is the he ratio of the vacuum velocity of light to the group velocity in a medium.
Barometric Pressure - Barometric Pressure is the pressure on earth that is caused by the weight of the air above us. It is sometimes the atmospheric pressure. It should be entered in millibar.
Temperature in Celsius - Temperature in Celsius is the degree of coolness or hotness of any substance. It should be entered in degree celsius.
Partial Pressure of Water Vapour - (Measured in Pascal) - Partial pressure of water vapour is the vapour pressure in any gas mixture in equilibrium with solid or liquid water.

STEP 1: Convert Input(s) to Base Unit

Barometric Pressure: 6921.213 --> No Conversion Required
Temperature in Celsius: 98 --> No Conversion Required
Partial Pressure of Water Vapour: 1006 Millibar --> 100600 Pascal (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

n = 1+(77.624*P_b*10^-6/(273.15+t))+((0.372/(273.15+t)^2)-(12.92*10^-6/(273.15+t)))*e --> 1+(77.624*6921.213*10^-6/(273.15+98))+((0.372/(273.15+98)^2)-(12.92*10^-6/(273.15+98)))*100600

Evaluating ... ...

n = 1.26961576791782

STEP 3: Convert Result to Output's Unit

1.26961576791782 --> No Conversion Required

FINAL ANSWER

1.26961576791782 ≈ 1.269616 <-- Group Refractive Index

(Calculation completed in 00.004 seconds)

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Home » Engineering » Civil » Surveying Formulas » Electromagnetic Distance Measurement » EDM Corrections » Essen and Froome Formula for Group Refractive Index

Credits

Created by Chandana P Dev

NSS College of Engineering (NSSCE), Palakkad

Chandana P Dev has created this Calculator and 500+ more calculators!

Verified by Ishita Goyal

Meerut Institute of Engineering and Technology (MIET), Meerut

Ishita Goyal has verified this Calculator and 2600+ more calculators!

< 11 EDM Corrections Calculators

Barometric Pressure given Group Refractive Index

Go Barometric Pressure = ((Group Refractive Index-1)+(((11.27*10^-6*Partial Pressure of Water Vapour)/(273.15+Temperature in Celsius))))*((273.15+Temperature in Celsius)/(0.269578*(Group Refractive Index for Standard Condition-1)))

Group Refractive Index if Temperature and Humidity are different from Standard Values

Go Group Refractive Index = 1+((0.269578*(Group Refractive Index for Standard Condition-1)*Barometric Pressure)/(273.15+Temperature in Celsius))-((11.27/(273.15+Temperature in Celsius))*10^-6*Partial Pressure of Water Vapour)

IUCG Formula for Refractive Index

Go Group Refractive Index = 1+(0.000077624*Barometric Pressure/(273.15+Temperature in Celsius))-(((12.924/(273.15+Temperature in Celsius))+(371900/(273.15+Temperature in Celsius)^2))*10^-6*Partial Pressure of Water Vapour)

Essen and Froome Formula for Group Refractive Index

Go Group Refractive Index = 1+(77.624*Barometric Pressure*10^-6/(273.15+Temperature in Celsius))+((0.372/(273.15+Temperature in Celsius)^2)-(12.92*10^-6/(273.15+Temperature in Celsius)))*Partial Pressure of Water Vapour

Overall Standard Error

Go Overall Standard Error = sqrt(Standard Error e^2+(Distance Traveled*Standard Error p*10^-6)^2)

Corrected Slope Distance for Refractive Index

Go Corrected Slope = (Standard Refractive Index/Refractive Index)*Measured Distance

Group Refractive Index at Standard Conditions

Go Group Refractive Index for Standard Condition = 1+(287.604+(4.8864/Wavelength^2)+(0.068/Wavelength^4))*10^-6

Temperature Difference given Partial Pressure

Go Temperature Change = (Saturated Vapor Pressure of Water-Partial Pressure of Water Vapour)/0.7

Partial Pressure of Water Vapour when Temperature Effects are Considered

Go Partial Pressure of Water Vapour = Saturated Vapor Pressure of Water-0.7*Temperature Change

Wave Velocity in Medium

Go Wave Velocity = Velocity in Vacuum/Refractive Index

Wave Velocity in Vacuum

Go Velocity in Vacuum = Wave Velocity*Refractive Index

Essen and Froome Formula for Group Refractive Index Formula

What is EDM Calibration?

An Electronic Distance Measurement (EDM) instrument is calibrated on a baseline to determine instrument constants and errors. A series of measurements on a baseline can also be used to check the performance and reliability of the instrument and to assess its precision against the manufacturer's claims.

How to Calculate Essen and Froome Formula for Group Refractive Index?

Essen and Froome Formula for Group Refractive Index calculator uses Group Refractive Index = 1+(77.624*Barometric Pressure*10^-6/(273.15+Temperature in Celsius))+((0.372/(273.15+Temperature in Celsius)^2)-(12.92*10^-6/(273.15+Temperature in Celsius)))*Partial Pressure of Water Vapour to calculate the Group Refractive Index, The Essen and Froome Formula for Group Refractive Index formula is defined as the refractive index value for microwaves. Here the temperature is represented in degrees Celsius or can directly substitute in kelvin. Group Refractive Index is denoted by n symbol.

How to calculate Essen and Froome Formula for Group Refractive Index using this online calculator? To use this online calculator for Essen and Froome Formula for Group Refractive Index, enter Barometric Pressure (P_b), Temperature in Celsius (t) & Partial Pressure of Water Vapour (e) and hit the calculate button. Here is how the Essen and Froome Formula for Group Refractive Index calculation can be explained with given input values -> 1.269616 = 1+(77.624*6921.213*10^-6/(273.15+98))+((0.372/(273.15+98)^2)-(12.92*10^-6/(273.15+98)))*100600.

FAQ

What is Essen and Froome Formula for Group Refractive Index?

The Essen and Froome Formula for Group Refractive Index formula is defined as the refractive index value for microwaves. Here the temperature is represented in degrees Celsius or can directly substitute in kelvin and is represented as n = 1+(77.624*P_b*10^-6/(273.15+t))+((0.372/(273.15+t)^2)-(12.92*10^-6/(273.15+t)))*e or Group Refractive Index = 1+(77.624*Barometric Pressure*10^-6/(273.15+Temperature in Celsius))+((0.372/(273.15+Temperature in Celsius)^2)-(12.92*10^-6/(273.15+Temperature in Celsius)))*Partial Pressure of Water Vapour. Barometric Pressure is the pressure on earth that is caused by the weight of the air above us. It is sometimes the atmospheric pressure. It should be entered in millibar, Temperature in Celsius is the degree of coolness or hotness of any substance. It should be entered in degree celsius & Partial pressure of water vapour is the vapour pressure in any gas mixture in equilibrium with solid or liquid water.

How to calculate Essen and Froome Formula for Group Refractive Index?

The Essen and Froome Formula for Group Refractive Index formula is defined as the refractive index value for microwaves. Here the temperature is represented in degrees Celsius or can directly substitute in kelvin is calculated using Group Refractive Index = 1+(77.624*Barometric Pressure*10^-6/(273.15+Temperature in Celsius))+((0.372/(273.15+Temperature in Celsius)^2)-(12.92*10^-6/(273.15+Temperature in Celsius)))*Partial Pressure of Water Vapour. To calculate Essen and Froome Formula for Group Refractive Index, you need Barometric Pressure (P_b), Temperature in Celsius (t) & Partial Pressure of Water Vapour (e). With our tool, you need to enter the respective value for Barometric Pressure, Temperature in Celsius & Partial Pressure of Water Vapour and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Group Refractive Index?

In this formula, Group Refractive Index uses Barometric Pressure, Temperature in Celsius & Partial Pressure of Water Vapour. We can use 2 other way(s) to calculate the same, which is/are as follows -

Group Refractive Index = 1+((0.269578*(Group Refractive Index for Standard Condition-1)*Barometric Pressure)/(273.15+Temperature in Celsius))-((11.27/(273.15+Temperature in Celsius))*10^-6*Partial Pressure of Water Vapour)
Group Refractive Index = 1+(0.000077624*Barometric Pressure/(273.15+Temperature in Celsius))-(((12.924/(273.15+Temperature in Celsius))+(371900/(273.15+Temperature in Celsius)^2))*10^-6*Partial Pressure of Water Vapour)

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