Foot-candles (ft-cd) to Lux (lx) conversion

What is Foot-candles?

Foot-candle is a non-SI unit of illuminance or light intensity. It measures the amount of light falling on a surface. Understanding foot-candles is crucial in fields like lighting design, photography, and horticulture.

Definition of Foot-candle

A foot-candle (fc) is defined as the illuminance on a one-square-foot surface from a uniform source of light of one candle (candela) at a distance of one foot. In simpler terms, it measures how much light a surface receives.

How Foot-candles Are Formed

Foot-candle is derived from the older English units system. The unit is based on the following components:

• Candela (cd): The base SI unit of luminous intensity, representing the power emitted by a light source in a particular direction.
• Foot (ft): A unit of length.
• Illuminance: Luminous flux incident on a surface per unit area.

The relationship can be expressed as:

$$1 \text{ fc} = 1 \frac{\text{lumen}}{\text{ft}^2}$$

Where a lumen is derived from candela.

$$\text{Lumen (lm)} = \text{Candela (cd)} \times \text{Steradian (sr)}$$

Relationship to Lux

Lux (lx) is the SI unit of illuminance. The relationship between foot-candle and lux is:

$$1 \text{ fc} \approx 10.764 \text{ lx}$$

Conversely:

$$1 \text{ lx} \approx 0.0929 \text{ fc}$$

Laws and People Associated

While no specific law is directly named after foot-candles, it is closely related to the inverse square law of light. This law states that the illuminance (E) is inversely proportional to the square of the distance (d) from the light source:

$$E \propto \frac{1}{d^2}$$

This means that as the distance from a light source doubles, the illuminance decreases to one-quarter of its original value.

Interesting Fact:

Historically, the definition of a "candle" was based on a specific type of wax candle. Over time, the definition was standardized using more precise measurements.

Real-World Examples

• Full Sunlight: Approximately 10,000 fc.
• Overcast Day: Around 100-1,000 fc.
• Office Lighting: Typically 20-50 fc.
• Hallways and Corridors: 5-10 fc.
• Moonlight: Roughly 0.01 fc.

Understanding these typical values can help in designing appropriate lighting systems for various environments. For further reading, you can explore resources such as the Illuminating Engineering Society (IES).

What is Lux?

Lux (symbol: lx) is the SI derived unit of illuminance, measuring luminous flux per unit area. It quantifies the amount of light falling on a surface. Essentially, it tells us how intensely a surface is being illuminated.

Definition and Formula

Lux is defined as one lumen per square meter. Mathematically:

$$1 \text{ lx} = 1 \frac{\text{lm}}{\text{m}^2} = 1 \frac{\text{cd} \cdot \text{sr}}{\text{m}^2}$$

Where:

• lx is lux
• lm is lumen (a measure of luminous flux)
• cd is candela (a measure of luminous intensity)
• sr is steradian (a measure of solid angle)
• $m^2$ is square meter

This means that if a light source with a luminous intensity of one candela shines uniformly onto a one-square-meter surface, and all of its light falls on that surface, the illuminance is one lux.

Formation of Lux

Lux is derived from the fundamental SI units of candela (cd) for luminous intensity and meter (m) for distance. The lumen (lm), which is used in the definition of lux, is itself derived from candela and steradian (sr). Therefore, lux ultimately relates luminous intensity to area.

Relationship to Luminous Flux and Distance

The illuminance decreases as the distance from the light source increases. This follows the inverse square law:

$$E = \frac{I}{d^2}$$

Where:

• $E$ is illuminance (in lux)
• $I$ is luminous intensity (in candela)
• $d$ is the distance from the light source (in meters)

This means that doubling the distance from a light source reduces the illuminance to one-quarter of its original value.

Interesting Facts and Associated Figures

While there isn't a specific "law of lux," the inverse square law described above is a fundamental principle governing how illuminance changes with distance.

The study of light and its measurement, including illuminance, has been advanced by numerous scientists throughout history. While no single person is exclusively "associated" with lux, figures like:

• André-Eugène Blondel: A French physicist and engineer who contributed significantly to photometry and lighting technology. His work helped standardize units and methods for measuring light.
• Arthur Holly Compton: An American physicist who won the Nobel Prize in Physics in 1927 for his discovery of the Compton effect, which demonstrated the particle nature of electromagnetic radiation (including light).

Real-World Examples of Lux Values

Understanding typical lux values can provide a sense of how bright different environments are:

• Full daylight: 10,000 - 25,000 lux
• Overcast day: 1,000 lux
• Office lighting: 300 - 500 lux
• Well-lit home: 100 - 300 lux
• Twilight: 10 lux
• Full moon: 0.25 lux
• Starlight: 0.0001 lux

These examples demonstrate the wide range of illuminance levels we experience in our daily lives. Proper lighting design aims to provide adequate illuminance for the tasks being performed in a space, balancing energy efficiency with visual comfort and safety. Refer to Illuminance Recommendations by the IES for industry standards.