Lambert's Cosine Law Calculator

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✖Illumination Intensity is defined as the number of lumens, falling on the surface, per unit area.ⓘ 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

`"0.66323"="0.8lx"*cos("34°")`

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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 - Trigonometric cosine function, 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 is defined as the number of lumens, falling on the surface, per unit area.
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: 0.8 Lux --> 0.8 Lux No Conversion Required
Incident Angle: 34 Degree --> 0.59341194567796 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

E_θ = E_v*cos(θ_i) --> 0.8*cos(0.59341194567796)

Evaluating ... ...

E_θ = 0.663230058044084

STEP 3: Convert Result to Output's Unit

0.663230058044084 --> No Conversion Required

FINAL ANSWER

0.663230058044084 <-- Illuminance at Angle of Incidence

(Calculation completed in 00.000 seconds)

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Created by Aman Dhussawat

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

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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

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 -> 0.66323 = 0.8*cos(0.59341194567796).

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 is defined as the number of lumens, falling on the surface, per unit area & 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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