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Lambert's Cosine Law Formula

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Illuminance at angle of incidence is also known as the illumination angle of a surface with a light source, such as the Earth's surface and the Sun. Check FAQs

E θ = E v \cdot \cos (θ i)

E_θ - Illuminance at Angle of Incidence?E_v - Illumination Intensity?θ_i - Incident Angle?

Lambert's Cosine Law Example

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Here is how the Lambert's Cosine Law equation looks like with Values.

Here is how the Lambert's Cosine Law equation looks like with Units.

Here is how the Lambert's Cosine Law equation looks like.

0.8833 = 1.02 \cdot \cos (30)

0.8833 = 1.02lx \cdot \cos (30°)

0.8833 = 1.02 \cdot \cos (30)

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Lambert's Cosine Law Solution

Follow our step by step solution on how to calculate Lambert's Cosine Law?

FIRST Step Consider the formula

E θ = E v \cdot \cos (θ i)

Next Step Substitute values of Variables

∴

E θ = 1.02lx \cdot \cos (30°)

Next Step Convert Units

∴

E θ = 1.02lx \cdot \cos (0.5236rad)

Next Step Prepare to Evaluate

∴

E θ = 1.02 \cdot \cos (0.5236)

Next Step Evaluate

∴

E θ = 0.883345911860127

LAST Step Rounding Answer

∴

E θ = 0.8833

Lambert's Cosine Law Formula Elements

Variables

Functions

Illuminance at Angle of Incidence

Illuminance at angle of incidence is also known as the illumination angle of a surface with a light source, such as the Earth's surface and the Sun.

Symbol: E_θ

Measurement: NAUnit: Unitless

Note: Value can be positive or negative.

Formulas to find Illuminance at Angle of Incidence

Illumination Intensity

Illumination intensity refers to the level or strength of light in a given area. It quantifies the amount of light reaching a surface and is typically measured in units such as lux or foot-candles.

Symbol: E_v

Measurement: IlluminanceUnit: lx

Note: Value can be positive or negative.

Formulas to find Illumination Intensity

Incident Angle

The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.

Symbol: θ_i

Measurement: AngleUnit: °

Note: Value can be positive or negative.

Formulas to find Incident Angle

cos

Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle.

Syntax: cos(Angle)

Other formulas in Laws of Illumination category

Go Specific Consumption

S.C. = \frac{2 \cdot P in}{CP}

Go Utilization Factor of Electrical Energy

UF = \frac{L r}{L e}

Go Luminous Intensity

I v = \frac{Lm}{ω}

Go Beer-Lambert Law

I t = I o \cdot \exp (- β \cdot c \cdot x)

How to Evaluate Lambert's Cosine Law?

Lambert's Cosine Law evaluator uses Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle) to evaluate the Illuminance at Angle of Incidence, The Lambert's Cosine Law formula is defined as Lambert’s cosine law states that the radiant intensity from the ideal diffusely reflecting surface and cosine of the angle θ between the direction of incident light and surface normal are directly proportional. Illuminance at Angle of Incidence is denoted by E_θ symbol.

How to evaluate Lambert's Cosine Law using this online evaluator? To use this online evaluator for Lambert's Cosine Law, enter Illumination Intensity (E_v) & Incident Angle (θ_i) and hit the calculate button.

FAQs on Lambert's Cosine Law

What is the formula to find Lambert's Cosine Law?

The formula of Lambert's Cosine Law is expressed as Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle). Here is an example- 0.883346 = 1.02*cos(0.5235987755982).

How to calculate Lambert's Cosine Law?

With Illumination Intensity (E_v) & Incident Angle (θ_i) we can find Lambert's Cosine Law using the formula - Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle). This formula also uses Cosine function(s).

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Lambert's Cosine Law Formula

Lambert's Cosine Law Example

Lambert's Cosine Law Solution

Lambert's Cosine Law Formula Elements

Other formulas in Laws of Illumination category

How to Evaluate Lambert's Cosine Law?

FAQs on Lambert's Cosine Law

Variable Name