Beam Divergence Solution

STEP 0: Pre-Calculation Summary
Formula Used
Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration))
α = sqrt((4*P)/(pi*flens^2*δp*ΔT))
This formula uses 1 Constants, 1 Functions, 5 Variables
Constants Used
pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288
Functions Used
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)
Variables Used
Beam Divergence - (Measured in Radian) - Beam Divergence is the angle made by the beam incident on surface of metal.
Laser Energy Output - (Measured in Watt) - Laser Energy Output is the output energy of the laser used in LBM.
Focal Length of Lens - (Measured in Meter) - Focal Length of Lens is determined when lens is focused at infinity. Lens focal length tells us angle of view and how much of scene will be captured. The longer focal length, a narrower angle of view.
Power Density of Laser Beam - (Measured in Watt per Square Meter) - Power Density of Laser Beam is the power per unit area of beam.
Laser Beam Duration - (Measured in Second) - Laser Beam Duration is the time for which laser beam is incident on the work surface.
STEP 1: Convert Input(s) to Base Unit
Laser Energy Output: 10.39 Watt --> 10.39 Watt No Conversion Required
Focal Length of Lens: 3 Meter --> 3 Meter No Conversion Required
Power Density of Laser Beam: 9.49 Watt per Square Centimeter --> 94900 Watt per Square Meter (Check conversion here)
Laser Beam Duration: 10.2 Second --> 10.2 Second No Conversion Required
STEP 2: Evaluate Formula
Substituting Input Values in Formula
α = sqrt((4*P)/(pi*flens^2*δp*ΔT)) --> sqrt((4*10.39)/(pi*3^2*94900*10.2))
Evaluating ... ...
α = 0.00123227712391686
STEP 3: Convert Result to Output's Unit
0.00123227712391686 Radian --> No Conversion Required
FINAL ANSWER
0.00123227712391686 0.001232 Radian <-- Beam Divergence
(Calculation completed in 00.020 seconds)

Credits

Created by Rajat Vishwakarma
University Institute of Technology RGPV (UIT - RGPV), Bhopal
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Verified by Nishan Poojary
Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi
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8 Power density of laser beam Calculators

Focal Length of Lens
Go Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi* Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration))
Beam Divergence
Go Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration))
Power Density of Laser Beam
Go Power Density of Laser Beam = (4*Laser Energy Output)/(pi*Focal Length of Lens^2*Beam Divergence^2*Laser Beam Duration)
Pulse Duration of Laser
Go Laser Beam Duration = (4*Laser Energy Output)/(pi*Focal Length of Lens^2*Beam Divergence^2*Power Density of Laser Beam)
Laser Energy Output
Go Laser Energy Output = (Power Density of Laser Beam*pi*Focal Length of Lens^2*Beam Divergence^2*Laser Beam Duration)/4
Beam Divergence given Diameter of Spot
Go Beam Divergence = Spot Diameter/Focal Length of Lens
Focal Length given Diameter of Spot
Go Focal Length of Lens = Spot Diameter/Beam Divergence
Diameter of Spot Produced by Laser
Go Spot Diameter = Focal Length of Lens*Beam Divergence

Beam Divergence Formula

Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration))
α = sqrt((4*P)/(pi*flens^2*δp*ΔT))

How does Laser Beam Machining work ?

Laser (light amplification by stimulated emission of radiation) beam machining (LBM) utilises the energy from the coherent light beams called laser (light amplification by stimulated emission of radiation). The basic principle utilised in LBM is that under proper conditions light energy of a particular frequency is used to stimulate the electrons in an atom to emit additional light with exactly the same characteristics of the original light source.

How to Calculate Beam Divergence?

Beam Divergence calculator uses Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)) to calculate the Beam Divergence, The Beam divergence formula is defined as the angle of divergence of the laser beam used in Laser beam machining. Beam Divergence is denoted by α symbol.

How to calculate Beam Divergence using this online calculator? To use this online calculator for Beam Divergence, enter Laser Energy Output (P), Focal Length of Lens (flens), Power Density of Laser Beam p) & Laser Beam Duration (ΔT) and hit the calculate button. Here is how the Beam Divergence calculation can be explained with given input values -> 0.001232 = sqrt((4*10.39)/(pi*3^2*94900*10.2)).

FAQ

What is Beam Divergence?
The Beam divergence formula is defined as the angle of divergence of the laser beam used in Laser beam machining and is represented as α = sqrt((4*P)/(pi*flens^2*δp*ΔT)) or Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)). Laser Energy Output is the output energy of the laser used in LBM, Focal Length of Lens is determined when lens is focused at infinity. Lens focal length tells us angle of view and how much of scene will be captured. The longer focal length, a narrower angle of view, Power Density of Laser Beam is the power per unit area of beam & Laser Beam Duration is the time for which laser beam is incident on the work surface.
How to calculate Beam Divergence?
The Beam divergence formula is defined as the angle of divergence of the laser beam used in Laser beam machining is calculated using Beam Divergence = sqrt((4*Laser Energy Output)/(pi*Focal Length of Lens^2*Power Density of Laser Beam*Laser Beam Duration)). To calculate Beam Divergence, you need Laser Energy Output (P), Focal Length of Lens (flens), Power Density of Laser Beam p) & Laser Beam Duration (ΔT). With our tool, you need to enter the respective value for Laser Energy Output, Focal Length of Lens, Power Density of Laser Beam & Laser Beam Duration 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 Beam Divergence?
In this formula, Beam Divergence uses Laser Energy Output, Focal Length of Lens, Power Density of Laser Beam & Laser Beam Duration. We can use 1 other way(s) to calculate the same, which is/are as follows -
  • Beam Divergence = Spot Diameter/Focal Length of Lens
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