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Focal Length of Lens Formula

GoFocal Length given Diameter of Spot Formula

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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. Check FAQs

f lens = \sqrt{\frac{4 \cdot P}{π \cdot δ p \cdot α^{2} \cdot ΔT}}

f_lens - Focal Length of Lens?P - Laser Energy Output?δ_p - Power Density of Laser Beam?α - Beam Divergence?ΔT - Laser Beam Duration?π - Archimedes' constant?

Focal Length of Lens Example

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Here is how the Focal Length of Lens equation looks like with Values.

Here is how the Focal Length of Lens equation looks like with Units.

Here is how the Focal Length of Lens equation looks like.

3.0007 = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 9.49 \cdot {0.0012}^{2} \cdot 10.2}}

3.0007m = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot 9.49W/cm² \cdot {0.0012rad}^{2} \cdot 10.2s}}

3.0007 = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 9.49 \cdot {0.0012}^{2} \cdot 10.2}}

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Focal Length of Lens Solution

Follow our step by step solution on how to calculate Focal Length of Lens?

FIRST Step Consider the formula

f lens = \sqrt{\frac{4 \cdot P}{π \cdot δ p \cdot α^{2} \cdot ΔT}}

Next Step Substitute values of Variables

∴

f lens = \sqrt{\frac{4 \cdot 10.39W}{π \cdot 9.49W/cm² \cdot {0.0012rad}^{2} \cdot 10.2s}}

Next Step Substitute values of Constants

∴

f lens = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot 9.49W/cm² \cdot {0.0012rad}^{2} \cdot 10.2s}}

Next Step Convert Units

∴

f lens = \sqrt{\frac{4 \cdot 10.39W}{3.1416 \cdot 94900W/m² \cdot {0.0012rad}^{2} \cdot 10.2s}}

Next Step Prepare to Evaluate

∴

f lens = \sqrt{\frac{4 \cdot 10.39}{3.1416 \cdot 94900 \cdot {0.0012}^{2} \cdot 10.2}}

Next Step Evaluate

∴

f lens = 3.00067481473261m

LAST Step Rounding Answer

∴

f lens = 3.0007m

Focal Length of Lens Formula Elements

Variables

Constants

Functions

Focal Length of Lens

Symbol: f_lens

Measurement: LengthUnit: m

Note: Value should be greater than 0.

Formulas to find Focal Length of Lens

Laser Energy Output

Laser Energy Output refers to the amount of energy emitted by a laser over a specific period of time.

Symbol: P

Measurement: PowerUnit: W

Note: Value should be greater than 0.

Formulas to find Laser Energy Output

Power Density of Laser Beam

Power Density of Laser Beam is the power per unit area of beam.

Symbol: δ_p

Measurement: Heat Flux DensityUnit: W/cm²

Note: Value should be greater than 0.

Formulas to find Power Density of Laser Beam

Beam Divergence

Beam Divergence is the angle made by the beam incident on surface of metal.

Symbol: α

Measurement: AngleUnit: rad

Note: Value should be greater than 0.

Formulas to find Beam Divergence

Laser Beam Duration

Laser Beam Duration is the time for which laser beam is incident on the work surface.

Symbol: ΔT

Measurement: TimeUnit: s

Note: Value should be greater than 0.

Formulas to find Laser Beam Duration

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

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.

Syntax: sqrt(Number)

Other Formulas to find Focal Length of Lens

Go Focal Length given Diameter of Spot

f lens = \frac{d spot}{α}

Other formulas in Power Density of Laser Beam category

Go Power Density of Laser Beam

δ p = \frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot α^{2} \cdot ΔT}

Go Laser Energy Output

P = \frac{δ p \cdot π \cdot {f lens}^{2} \cdot α^{2} \cdot ΔT}{4}

Go Beam Divergence

α = \sqrt{\frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot δ p \cdot ΔT}}

Go Pulse Duration of Laser

ΔT = \frac{4 \cdot P}{π \cdot {f lens}^{2} \cdot α^{2} \cdot δ p}

How to Evaluate Focal Length of Lens?

Focal Length of Lens evaluator uses Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi*Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)) to evaluate 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 evaluate Focal Length of Lens using this online evaluator? To use this online evaluator 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.

FAQs on Focal Length of Lens

What is the formula to find Focal Length of Lens?

The formula of Focal Length of Lens is expressed as Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi*Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)). Here is an example- 3.000676 = sqrt((4*10.39)/(pi*94900*0.001232^2*10.2)).

How to calculate Focal Length of Lens?

With Laser Energy Output (P), Power Density of Laser Beam (δ_p), Beam Divergence (α) & Laser Beam Duration (ΔT) we can find Focal Length of Lens using the formula - Focal Length of Lens = sqrt((4*Laser Energy Output)/(pi*Power Density of Laser Beam*Beam Divergence^2*Laser Beam Duration)). This formula also uses Archimedes' constant and Square Root (sqrt) function(s).

What are the other ways to Calculate Focal Length of Lens?

Here are the different ways to Calculate Focal Length of Lens-

Focal Length of Lens=Spot Diameter/Beam Divergence

Can the Focal Length of Lens be negative?

No, the Focal Length of Lens, measured in Length cannot be negative.

Which unit is used to measure Focal Length of Lens?

Focal Length of Lens is usually measured using the Meter[m] for Length. Millimeter[m], Kilometer[m], Decimeter[m] are the few other units in which Focal Length of Lens can be measured.

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Focal Length of Lens Formula

​GoFocal Length given Diameter of Spot Formula

Focal Length of Lens Example

Focal Length of Lens Solution

Focal Length of Lens Formula Elements

Other Formulas to find Focal Length of Lens

Other formulas in Power Density of Laser Beam category

How to Evaluate Focal Length of Lens?

FAQs on Focal Length of Lens

Variable Name

GoFocal Length given Diameter of Spot Formula