Luminous Efficiency & Intensity
How efficiently a lamp makes light, and how much it sends in each direction.
Lesson at a glanceShow the key points
- Luminous efficiency = total luminous flux / total radiant flux (22.1); 685 lm/W for 555 nm by definition.
- Overall luminous efficiency of a lamp = luminous flux / electrical power input (22.2); filament lamps rarely exceed 50 lm/W.
- Solid angle ω = A/R² (steradian, sr); a whole sphere is 4π sr.
- Luminous intensity in a direction: I = dF/dω (22.3), unit candela (cd = lm/sr), one of the SI base units. A uniform point source: I = F/4π.
A lamp’s packaging gives its lumens; a torch is rated by how much light it throws in one direction. These are two different quantities, and the second needs the idea of a solid angle.
Luminous efficiency
For a lamp, what matters is how well the electrical power becomes brightness:
A filament lamp wastes much of its power heating the filament, and much of its radiation is infrared, which the eye can’t see. Its overall efficiency is rarely above about 50 lm/W.
Solid angle
Luminous intensity
The luminous intensity of a source in a given direction is the luminous flux per unit solid angle sent in that direction:
An ideal point source radiates equally in all directions, so . Real, extended sources have different intensities in different directions. Luminous intensity is also called illuminating power.
A small disc of radius 1.5 cm, 3.0 m from a uniformly radiating point source and facing it, receives 6.0 × 10⁻³ lm. Find the source’s intensity and total flux.
A 60 W lamp has an overall luminous efficiency of 15 lm/W and emits evenly into the forward half-space only. How much flux falls on a 4.0 cm² card 0.40 m away, facing it?
- 1Luminous efficiency = luminous flux / radiant flux; overall efficiency = luminous flux / power input.
- 2Solid angle ω = A/R² (steradian); whole sphere 4π sr.
- 3Luminous intensity I = dF/dω, in candela; a uniform point source has I = F/4π.
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Keep exploring
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