Lambert's Cosine Law Calculator

✖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.ⓘ Illumination Intensity [E_v]			+10% -10%
✖The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.ⓘ Incident Angle [θ_i]			+10% -10%

✖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.ⓘ Lambert's Cosine Law [E_θ]

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Formula

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Lambert's Cosine Law

Formula

`"E"_{"θ"} = "E"_{"v"}*cos("θ"_{"i"})`

Example

`"0.883346"="1.02lx"*cos("30°")`

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Lambert's Cosine Law Solution

STEP 0: Pre-Calculation Summary

Formula Used

Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)
E_θ = E_v*cos(θ_i)
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

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.
Illumination Intensity - (Measured in Lux) - 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.
Incident Angle - (Measured in Radian) - The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.

STEP 1: Convert Input(s) to Base Unit

Illumination Intensity: 1.02 Lux --> 1.02 Lux No Conversion Required
Incident Angle: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_θ = E_v*cos(θ_i) --> 1.02*cos(0.5235987755982)

Evaluating ... ...

E_θ = 0.883345911860127

STEP 3: Convert Result to Output's Unit

0.883345911860127 --> No Conversion Required

FINAL ANSWER

0.883345911860127 ≈ 0.883346 <-- Illuminance at Angle of Incidence

(Calculation completed in 00.004 seconds)

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Home » Engineering » Electrical » Utilization of Electrical Energy » Illumination » Laws of Illumination » Lambert's Cosine Law

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Created by Aman Dhussawat

GURU TEGH BAHADUR INSTITUTE OF TECHNOLOGY (GTBIT), NEW DELHI

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Chandigarh University (CU), Punjab

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< 7 Laws of Illumination Calculators

Beer-Lambert Law

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption per Concentration Coefficient*Concentration of Absorption Material*Path Length)

Fresnel's Law of Reflection

Go Reflection Loss = (Refractive Index of Medium 2-Refractive Index of Medium 1)^2/(Refractive Index of Medium 2+Refractive Index of Medium 1)^2

Refracted Angle using Snell's Law

Go Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))

Incident Angle using Snell's Law

Go Incident Angle = arcsinh((Refractive Index of Medium 2*sin(Refracted Angle))/(Refractive Index of Medium 1))

Illumination by Lambert Cosine Law

Go Illumination Intensity = (Luminous Intensity*cos(Illumination Angle))/(Length of Illumination^2)

Lambert's Cosine Law

Go Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)

Inverse Square Law

Go Luminance = Intensity of Transmitted Light/Distance^2

< 16 Advanced Illumination Calculators

Beer-Lambert Law

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption per Concentration Coefficient*Concentration of Absorption Material*Path Length)

Fresnel's Law of Reflection

Go Reflection Loss = (Refractive Index of Medium 2-Refractive Index of Medium 1)^2/(Refractive Index of Medium 2+Refractive Index of Medium 1)^2

Refracted Angle using Snell's Law

Go Refracted Angle = arcsinh((Refractive Index of Medium 1*sin(Incident Angle))/(Refractive Index of Medium 2))

Incident Angle using Snell's Law

Go Incident Angle = arcsinh((Refractive Index of Medium 2*sin(Refracted Angle))/(Refractive Index of Medium 1))

Intensity of Light Transmitted

Go Intensity of Transmitted Light = Intensity of Light Entering the Material*exp(-Absorption Coefficient*Path Length)

Illumination by Lambert Cosine Law

Go Illumination Intensity = (Luminous Intensity*cos(Illumination Angle))/(Length of Illumination^2)

Number of Floodlighting Units

Go Number of Floodlighting Units = (Area to be Lighted*Illumination Intensity)/(0.7*Lumen Flux)

Lambert's Cosine Law

Go Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)

Spectral Transmission Factor

Go Spectral Transmission Factor = Transmitted Spectral Emission/Spectral Irradiation

Spectral Reflection Factor

Go Spectral Reflection Factor = Reflected Spectral Emission/Spectral Irradiation

Utilization Factor of Electrical Energy

Go Utilization Factor = Lumen Reaching Working Plane/Lumen Emitting from Source

Spectral Luminous Efficacy

Go Spectral Luminous Efficacy = Maximum Sensitivity*Photopic Efficiency Value

Inverse Square Law

Go Luminance = Intensity of Transmitted Light/Distance^2

Specific Consumption

Go Specific Consumption = (2*Input Power)/Candle Power

Luminance for Lambertian Surfaces

Go Luminance = Illumination Intensity/pi

Luminous Intensity

Go Luminous Intensity = Lumen/Solid Angle

Lambert's Cosine Law Formula

Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle)
E_θ = E_v*cos(θ_i)

What is the importance of Lambert's cosine law?

The importance of Lambert's cosine law is that when a surface is viewed from any angle then it appears to be uniformly radian

How to Calculate Lambert's Cosine Law?

Lambert's Cosine Law calculator uses Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle) to calculate 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 calculate Lambert's Cosine Law using this online calculator? To use this online calculator for Lambert's Cosine Law, enter Illumination Intensity (E_v) & Incident Angle (θ_i) and hit the calculate button. Here is how the Lambert's Cosine Law calculation can be explained with given input values -> 0.883346 = 1.02*cos(0.5235987755982).

FAQ

What is Lambert's Cosine Law?

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 and is represented as E_θ = E_v*cos(θ_i) or Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle). 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 & The incident angle refers to the angle between the impact direction and the solid surface. For a vertical impact, this angle is 90 degrees.

How to calculate Lambert's Cosine Law?

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 is calculated using Illuminance at Angle of Incidence = Illumination Intensity*cos(Incident Angle). To calculate Lambert's Cosine Law, you need Illumination Intensity (E_v) & Incident Angle (θ_i). With our tool, you need to enter the respective value for Illumination Intensity & Incident Angle and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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