Luminous Intensity In Direction At Angle Calculator

Luminous Intensity Formula:

\[ I_\theta = L_n \times A \times \cos(\theta) \]

Luminous Intensity at Angle (I_θ):

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1. What is Luminous Intensity at Angle?

Luminous Intensity at Angle is defined as a measure of the wavelength-weighted power emitted by a light source in a particular direction at a specific angle θ. It quantifies how much light is emitted in a given direction relative to the surface normal.

2. How Does the Calculator Work?

The calculator uses the luminous intensity formula:

\[ I_\theta = L_n \times A \times \cos(\theta) \]

Where:

\( I_\theta \) — Luminous Intensity at Angle (Candela)
\( L_n \) — Luminance Normal to Surface (Lux)
\( A \) — Surface Area (m²)
\( \theta \) — Angle to Normal (degrees)
\( \cos \) — Cosine trigonometric function

Explanation: The formula calculates how the luminous intensity varies with the angle from the normal direction, following Lambert's cosine law.

3. Importance of Luminous Intensity Calculation

Details: Accurate luminous intensity calculation is crucial for lighting design, photometric analysis, and determining how light distribution varies with viewing angle in various applications.

4. Using the Calculator

Tips: Enter luminance normal to surface in Lux, surface area in square meters, and angle to normal in degrees (0-90). All values must be valid positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is the physical significance of luminous intensity at angle?
A: It describes how the perceived brightness of a surface changes when viewed from different angles, following the cosine distribution law.

Q2: Why does luminous intensity decrease with increasing angle?
A: According to Lambert's cosine law, the apparent area of the light-emitting surface decreases as the cosine of the viewing angle, reducing the perceived intensity.

Q3: What are typical units for luminous intensity?
A: Luminous intensity is measured in candela (cd), which is the SI base unit for luminous intensity.

Q4: How does this relate to illuminance and luminance?
A: Luminous intensity describes light emission in a specific direction, while illuminance measures light falling on a surface, and luminance describes light emitted from a surface.

Q5: What types of surfaces follow this cosine law?
A: Lambertian surfaces (perfectly diffuse reflectors/emitters) follow this law exactly, while other surfaces may have different angular distribution patterns.