1. What is Lambert's Cosine Law?

Lambert's Cosine Law states that the illuminance or luminous flux incident on a surface is directly proportional to the cosine of the angle between the direction of the incident light and the normal to the surface. This fundamental principle in photometry describes how illumination decreases as the angle of incidence increases.

2. How Does the Calculator Work?

The calculator uses Lambert's Cosine Law equation:

Where:

• \( E_{\theta} \) — Illuminance at angle of incidence (Lux)
• \( E_v \) — Illumination intensity (Lux)
• \( \theta_i \) — Incident angle (degrees)

Explanation: The equation shows that the illuminance on a surface decreases as the angle between the light source and the surface normal increases, following a cosine relationship.

3. Importance of Lambert's Cosine Law

Details: This law is crucial in lighting design, photography, computer graphics, and various optical applications. It helps predict how light intensity varies with surface orientation and is fundamental to understanding surface illumination in real-world scenarios.

4. Using the Calculator

Tips: Enter illumination intensity in Lux and incident angle in degrees (0-90°). The angle should be between the light direction and the surface normal. All values must be valid (intensity > 0, angle between 0-90 degrees).

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of Lambert's Cosine Law?
A: It describes how the apparent brightness of a surface decreases as the viewing angle increases from normal incidence, which is fundamental to understanding surface illumination and reflectance.

Q2: When does Lambert's Cosine Law apply?
A: It applies to perfectly diffuse (Lambertian) surfaces where light is scattered equally in all directions, and for point light sources at sufficient distance.

Q3: What are typical units for illuminance measurement?
A: Illuminance is typically measured in lux (lumens per square meter) or foot-candles (lumens per square foot).

Q4: How does surface orientation affect illumination?
A: As the surface tilts away from perpendicular to the light source, the same amount of light spreads over a larger area, reducing illuminance according to the cosine of the angle.

Q5: Are there limitations to Lambert's Cosine Law?
A: The law assumes ideal diffuse surfaces and may not perfectly apply to specular surfaces or complex lighting conditions with multiple light sources or reflections.