Focal Length of Lens Calculator

✖Laser Energy Output is the output energy of the laser used in LBM.ⓘ Laser Energy Output [P]			+10% -10%
✖Power Density of Laser Beam is the power per unit area of beam.ⓘ Power Density of Laser Beam [δ_p]			+10% -10%
✖Beam Divergence is the angle made by the beam incident on surface of metal.ⓘ Beam Divergence [α]			+10% -10%
✖Laser Beam Duration is the time for which laser beam is incident on the work surface.ⓘ Laser Beam Duration [ΔT]			+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]

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Formula

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Focal Length of Lens

Formula

`"f"_{"lens"} = sqrt((4*"P")/(pi* "δ"_{"p"}*"α"^2*"ΔT"))`

Example

`"3.000675m"=sqrt((4*"10.39W")/(pi* "9.49W/cm²"*("0.001232rad")^2*"10.20s"))`

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Focal Length of Lens Solution

STEP 0: Pre-Calculation Summary

Formula Used

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

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.
Laser Energy Output - (Measured in Watt) - Laser Energy Output is the output energy of the laser used in LBM.
Power Density of Laser Beam - (Measured in Watt per Square Meter) - Power Density of Laser Beam is the power per unit area of beam.
Beam Divergence - (Measured in Radian) - Beam Divergence is the angle made by the beam incident on surface of metal.
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
Power Density of Laser Beam: 9.49 Watt per Square Centimeter --> 94900 Watt per Square Meter (Check conversion here)
Beam Divergence: 0.001232 Radian --> 0.001232 Radian No Conversion Required
Laser Beam Duration: 10.2 Second --> 10.2 Second No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

f_lens = sqrt((4*P)/(pi* δ_p*α^2*ΔT)) --> sqrt((4*10.39)/(pi* 94900*0.001232^2*10.2))

Evaluating ... ...

f_lens = 3.00067481473261

STEP 3: Convert Result to Output's Unit

3.00067481473261 Meter --> No Conversion Required

FINAL ANSWER

3.00067481473261 ≈ 3.000675 Meter <-- Focal Length of Lens

(Calculation completed in 00.020 seconds)

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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

Nishan Poojary has verified this Calculator and 400+ more calculators!

< 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

Focal Length of Lens Formula

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

Focal Length of Lens calculator uses Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi* Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)) to calculate the Focal Length of Lens, The Focal length of lens formula is defined as a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. Focal Length of Lens is denoted by f_lens symbol.

How to calculate Focal Length of Lens using this online calculator? To use this online calculator for Focal Length of Lens, enter Laser Energy Output (P), Power Density of Laser Beam (δ_p), Beam Divergence (α) & Laser Beam Duration (ΔT) and hit the calculate button. Here is how the Focal Length of Lens calculation can be explained with given input values -> 3.000676 = sqrt((4*10.39)/(pi* 94900*0.001232^2*10.2)).

FAQ

What is Focal Length of Lens?

The Focal length of lens formula is defined as a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light and is represented as f_lens = sqrt((4*P)/(pi* δ_p*α^2*ΔT)) or Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi* Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)). Laser Energy Output is the output energy of the laser used in LBM, Power Density of Laser Beam is the power per unit area of beam, Beam Divergence is the angle made by the beam incident on surface of metal & Laser Beam Duration is the time for which laser beam is incident on the work surface.

How to calculate Focal Length of Lens?

The Focal length of lens formula is defined as a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light is calculated using Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi* Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)). To calculate Focal Length of Lens, you need Laser Energy Output (P), Power Density of Laser Beam (δ_p), Beam Divergence (α) & Laser Beam Duration (ΔT). With our tool, you need to enter the respective value for Laser Energy Output, Power Density of Laser Beam, Beam Divergence & 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 Focal Length of Lens?

In this formula, Focal Length of Lens uses Laser Energy Output, Power Density of Laser Beam, Beam Divergence & Laser Beam Duration. We can use 1 other way(s) to calculate the same, which is/are as follows -

Focal Length of Lens = Spot Diameter/Beam Divergence

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