Illumination By Lambert Cosine Law Calculator

Lambert Cosine Law Equation:

\[ E_v = \frac{I_v \times \cos(\theta)}{L^2} \]

Luminous Intensity (Iv):

Candela

Illumination Angle (θ):

Radians

Length of Illumination (L):

Meters

Illumination Intensity (Ev):

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1. What is Lambert Cosine Law?

Lambert Cosine Law describes how the illumination intensity on a surface varies with the angle of incidence of the light. It states that the illuminance on a surface is proportional to the cosine of the angle between the light direction and the surface normal.

2. How Does the Calculator Work?

The calculator uses the Lambert Cosine Law equation:

\[ E_v = \frac{I_v \times \cos(\theta)}{L^2} \]

Where:

\( E_v \) — Illumination Intensity (Lux)
\( I_v \) — Luminous Intensity (Candela)
\( \theta \) — Illumination Angle (Radians)
\( L \) — Length of Illumination (Meters)

Explanation: The equation calculates the illuminance on a surface based on the light source's intensity, the angle of incidence, and the distance from the light source.

3. Importance of Illumination Intensity Calculation

Details: Accurate illumination intensity calculation is crucial for lighting design, architectural planning, photography, and ensuring proper visibility and comfort in various environments.

4. Using the Calculator

Tips: Enter luminous intensity in candela, illumination angle in radians, and length of illumination in meters. All values must be valid (intensity > 0, length > 0).

5. Frequently Asked Questions (FAQ)

Q1: What is the relationship between angle and illumination?
A: As the angle of incidence increases (moves away from perpendicular), the illumination intensity decreases according to the cosine of the angle.

Q2: What are typical illumination intensity values?
A: Typical values range from 10-50 lux for general ambient lighting to 500-1000 lux for task lighting in offices and workspaces.

Q3: Why is distance squared in the denominator?
A: This follows the inverse square law - illumination intensity decreases with the square of the distance from the light source.

Q4: Can this calculator be used for any light source?
A: Yes, the Lambert Cosine Law applies to all light sources that follow Lambertian distribution characteristics.

Q5: How does surface orientation affect illumination?
A: Surface orientation directly affects the angle of incidence, which in turn affects the illumination intensity according to the cosine relationship.