Illuminance

Illuminance, measured in lux, describes the amount of light illuminating a given surface. This measurement is to be distinguished from luminance, which measures the amount of light emitted or reflected by a surface in a specific direction.

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How to measure it in class

The ambient light sensor on the front of the smartphone, next to the front camera, is used by FizziQ as a luxmeter and makes it possible to verify experimentally how illuminance decreases with distance.

Steps:

• Locate the light sensor at the top of the smartphone’s screen, then open the illuminance measurement in FizziQ.
• Darken the room and record the residual illuminance: this is the zero to subtract from all subsequent measurements.
• Place a point-like lamp facing the sensor, at a distance d measured with a ruler, with the smartphone’s screen exactly perpendicular to the direction of the lamp.
• Record the illuminance for about ten distances between 10 cm and 1 m, keeping the lamp and the sensor aligned.
• Plot E against 1/d²: the points should line up on a straight line through the origin. A plot of E against d, on the other hand, proves nothing.
• Repeat while tilting the smartphone: the illuminance drops as the cosine of the angle of incidence, which explains the weakness of solar illuminance in winter.

Scientific activities on this topic

Many experiments available in the FizziQ app and feasible with a smartphone help students better understand the various characteristics of light, in particular the notions of illuminance and luminance.

• Illuminance and distance from the source, to establish the 1/d² law
• Safety and visibility, diffusion and retroreflection of materials
• Measuring the solar constant with a pyrheliometer

As an extension, the La main à la pâte Foundation offers a challenge on albedo and climate change (in French) that can be done with a luxmeter.

Learn more

In the FizziQ app, two main measurements are used for light: luminance and illuminance. The difference between these two measurements lies in what they measure and how they are perceived in the context of light and vision.

• Illuminance:

• Definition: Illuminance is a measure of the amount of light arriving on a surface. It quantifies how much light (luminous flux) is received per unit area.

• Unit: Measured in lux (lx), where one lux equals one lumen per square meter.

• Context of use: Illuminance is used to determine the illumination of a surface, such as how much light illuminates a desk or a street.

• Luminance:

• Definition: Luminance is a measure of the amount of light emitted or reflected by a surface in a specific direction. It relates to the perceived brightness of a source or a surface.

• Unit: Measured in candelas per square meter (cd/m²).

• Context of use: Luminance matters in the design of displays and billboards, and for assessing visibility and visual comfort.

The article Brightness or luminance? covers this distinction in detail.

Do not confuse illuminance and luminous intensity

This is the most frequent confusion. Luminous intensity I, in candelas (cd), characterizes the source: it is the luminous flux it emits per unit solid angle. Illuminance E, in lux (lx), characterizes the illuminated surface: it is the flux received per unit area, that is, one lumen per square meter. The same lamp always has the same intensity in candelas, but the illuminance it produces changes as soon as you move it away or tilt the surface. In other words, the candela describes what leaves, the lux describes what arrives. The quantity common to both is the lumen (lm), the unit of luminous flux, the one that now appears on light bulb packaging in place of watts.

The 1/d² decrease, just like for sound

A point source emits its flux in all directions. At distance d, this flux is spread over a sphere of area 4πd². Since the area grows as d², the flux received per unit area decreases as 1/d². Doubling the distance divides the illuminance by four, not by two. It is exactly the same geometric reasoning as for the sound intensity of a point source, and it does not depend on any particular property of light: all that matters is the conservation of the flux over a growing sphere. The law assumes a source small compared with the distance; 10 cm from a one-meter fluorescent tube, it does not apply.

Add to this the effect of tilt: if the surface receives the light at an angle θ from its normal, the illuminance is multiplied by cos θ. This dependence is what explains why the Sun heats less in winter and at high latitudes, at an almost identical distance.

Orders of magnitude

Full-moon night: about 0.25 lx. Street lit at night: 10 to 20 lx. Properly lit classroom: 300 to 500 lx, the recommended value for desk work. Very bright office: 750 lx. Overcast sky in daytime: about 10,000 lx. Full summer sunlight: about 100,000 lx. The human eye therefore operates over a range of more than six orders of magnitude, which explains why a room seems “well lit” even though it receives a thousand times less light than outdoors.

Formula

Illuminance is the luminous flux received per unit area:

E = Φ/S

where:

• E: illuminance (lux, lx)
• Φ: luminous flux received by the surface (lumen, lm)
• S: area of the illuminated surface (m²)

For a point source of luminous intensity I, the illuminance of a surface perpendicular to the rays decreases as the square of the distance:

E = I/d²

where:

• I: luminous intensity of the source (candela, cd)
• d: distance between the source and the surface (m)

If the surface is tilted by an angle θ from the direction of the rays:

E = (I·cos θ)/d²

where:

• θ: angle between the normal to the surface and the direction of the source (rad or °)

Comparing two positions of the same source, the intensity cancels out:

E₁·d₁² = E₂·d₂²

Application examples

• A lamp produces 400 lx at 50 cm. At 1 m, it produces only 100 lx, since the illuminance is divided by 4 when the distance doubles.

• An LED bulb rated 800 lm lighting a 16 m² room uniformly provides an average illuminance of about 50 lx, far too little for reading: an additional desk lamp is needed.

• The solar constant is about 1,361 W/m² outside the atmosphere, corresponding to an illuminance of about 130,000 lx; at ground level, in clear weather, about 100,000 lx remains.

• The automatic brightness adjustment of a smartphone uses this very illuminance sensor: the screen dims in a dark room and brightens in sunlight.

• A retroreflective road sign sends the light of the headlights back toward the driver; the illuminance measured facing the sign is much higher than that of a sign simply painted white.

• On a north-facing balcony, the illuminance tops out at a few thousand lux even at the height of summer: the light arrives only by diffusion from the sky, never at direct incidence.

FAQ

Q: Can the lux values displayed by a smartphone be trusted? A: For relative comparisons, yes: measuring a ratio, a decrease, a doubling works very well. For an absolute value, no. The sensor is not calibrated, its spectral response differs from that of the human eye, and two phone models will give different numbers for the same scene. All the proposed activities therefore rely on ratios, not raw values.

Q: What is the difference between lux, lumen and candela? A: The lumen measures the total flux emitted or received. The candela measures the flux emitted per unit solid angle, a property of the source. The lux measures the flux received per square meter, a property of the illuminated surface. One lux equals one lumen per square meter.

Q: Why does illuminance decrease as 1/d² and not as 1/d? A: Because the emitted flux is spread over a sphere whose area is 4πd². It is the area, proportional to d², that grows, so the share received per square meter decreases accordingly. The same argument applies to the sound intensity of a point source.

Q: Why don’t my points line up on the line E = k/d²? A: Three frequent causes: the ambient light was not subtracted, the sensor is not exactly facing the lamp, or the lamp is too extended to be considered point-like at the distances used. Redo the measurement in the dark, locating the sensor’s position precisely.

Q: Is an illuminance of 500 lx strong or weak? A: It is the recommended value for a classroom, so comfortable for reading and writing. Yet it is still two hundred times lower than the illuminance in full sunlight. The eye adapts so well that these enormous differences go unnoticed.

Related concepts

Luminance - Luxmeter - Light sensor - Sound Intensity