Luminous Efficacy

Overview

Engineering reference data for Luminous Efficacy in miscellaneous.

Key Formulas

Unit Conversion

$y = x \cdot k$

Multiply by conversion factor.

Linear Interpolation

$y = y_1 + \frac{(x - x_1)(y_2 - y_1)}{x_2 - x_1}$

Estimate between two known points.

Percentage

$p = \frac{\text{part}}{\text{whole}} \times 100\%$

Part as fraction of whole.

Variables

Luminous Efficacy of Different Light Sources

Luminous Intensity

Luminous intensity measures the quantity of light radiated in a specific direction, which is particularly useful for directional lighting elements such as reflectors. It is defined as the luminous flux emitted per unit solid angle.

The relationship is given by:

$I = \frac{\Phi}{\Omega}$

where:

• $I$ is the luminous intensity (lm/sr, candela, cd),
• $\Phi$ is the luminous flux (lumen, lm),
• $\Omega$ is the solid angle (steradians, sr) into which the flux is emitted.

Example: Power Calculation for Light Sources

For an application requiring 500 lumens of light, the power consumption can be calculated using the luminous efficacy formula $P = \frac{\Phi}{\eta}$:

• For a tungsten incandescent lamp with luminous efficacy $\eta = 15 \text{ lm/W}$: $P = \frac{500 \text{ lm}}{15 \text{ lm/W}} = 33 \text{ W}$

• For an LED lamp with luminous efficacy $\eta = 70 \text{ lm/W}$: $P = \frac{500 \text{ lm}}{70 \text{ lm/W}} \approx 7.1 \text{ W}$

This illustrates how higher efficacy reduces power requirements for the same light output.

References

• Original Source