Beam Divergence Calculator

✖Laser Energy Output refers to the amount of energy emitted by a laser over a specific period of time.ⓘ Laser Energy Output [P]			+10% -10%
✖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.ⓘ Focal Length of Lens [f_lens]			+10% -10%
✖Power Density of Laser Beam is the power per unit area of beam.ⓘ Power Density of Laser Beam [δ_p]			+10% -10%
✖Laser Beam Duration is the time for which laser beam is incident on the work surface.ⓘ Laser Beam Duration [ΔT]			+10% -10%

✖Beam Divergence is the angle made by the beam incident on surface of metal.ⓘ Beam Divergence [α]

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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*f_lens^2*δ_p*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 refers to the amount of energy emitted by a laser over a specific period of time.
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*f_lens^2*δ_p*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 00.004 seconds)

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Home » Engineering » Production Engineering » Unconventional machining processes » Laser Beam Machining (LBM) » Power Density of Laser Beam » Beam Divergence

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Created by Rajat Vishwakarma

University Institute of Technology RGPV (UIT - RGPV), Bhopal

Rajat Vishwakarma has created this Calculator and 400+ more calculators!

Verified by Nishan Poojary

Shri Madhwa Vadiraja Institute of Technology and Management (SMVITM), Udupi

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< Power Density of Laser Beam Calculators

Focal Length of Lens

LaTeX Go Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi*Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration))

Beam Divergence

LaTeX 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

LaTeX Go Power Density of Laser Beam = (4*Laser Energy Output)/(pi*Focal Length of Lens^2*Beam Divergence^2*Laser Beam Duration)

Laser Energy Output

LaTeX Go Laser Energy Output = (Power Density of Laser Beam*pi*Focal Length of Lens^2*Beam Divergence^2*Laser Beam Duration)/4

Beam Divergence Formula

LaTeX Go

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*f_lens^2*δ_p*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 (f_lens), Power Density of Laser Beam (δ_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*f_lens^2*δ_p*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 refers to the amount of energy emitted by a laser over a specific period of time, 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 (f_lens), Power Density of Laser Beam (δ_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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