Experiment E10
Objectives:
1. To verify the inverse square and cosine laws of illumination for point sources
2. To relate illuminance ( illumination ) and luminance ( photometric brightness )
Apparatus:
0.2 metre ( 8 inch ) diameter opal glass sphere with 100 watt opal lamp GEC-SEI Portable Luxmeter or Kicke Digital Lightmeter
Sangamo rule and tape measure
Metre rule and tape measure
Hagner universal photometer
Asahi-Pentax spotmeter III
n.b. the voltage applied to the lamp need not be known providing it is constant throughout the experiment.
| 1 a) | Inverse
Square Law Measure the illuminance on a horizontal surface directly below the centre of the sphere at various distances ( measured from its centre to the floor ). Use the Hioki or GEC-SEI, meter to measure the illuminance. Calculate the luminous intensity of the sphere from I = Ed2 n.b. A perfectly diffusing shpere obeys the inverse square law at any distance. Take care to prevent reflected light from falling on the photocell or make a correction.
|
|
| b) | Cosine
Law Verify this by measuring the illuminance at a number of positions below the diffusing sphere but to one side, with the sphere at a height of one or two metres above the floor. Measure or calculate the angles of incidence for which the illuminance is measured, which should include angles up tp 60o. Note that an uncorrected photocell shows increased error at large angles of incidence. |
|
| 2 | Luminance
and Intensity Measure the luminance of the sphere and determine its luminous intensity from the relationship: L = intensity per unit projected area ( cd/m2 ) The projected area being ¶ x ( radius )2
|
|
| 3 | Luminance and Illuminance | |
| a) | Place a clean white
surface at a distance of 1 or 2 metres directly below the sphere. Calculate its
reflectance from the relationship: = ¶ L / E by measuring its luminance ( L cd/m2 ) for different valus of illuminance ( E lux ). The Asahi-Pentax spotmeter is an alternative instrument to the Hagner for measuring luminance. Use it to check the luminance measurement of the diffusing sphere and of the white surface below it.
|
|
| b) | Luminous exitance and
illuminance Measure the illuminance of an evenly-illuminanted section of the wall of the room. Compare this with the reading when the cell is placed about 15 cm from the wall, and facing it. The reflectance of the wall is given approximately by the ratio of the two readings. The second is the luminous exitance of the wall M lumens per metre2 or apostilb, þ = M/E. This method is only valid for matt diffusing surfaces. Compare the results against a colour chart for other surfaces in the room.
|
|
| 4 | Total
Luminous Flux By measuring the average luminance of the diffusing sphere, calculate its mean shperical intensity, and thence the total luminous flux ( F lumens ). By comparing this with the rated light output of the lamp estimate the light output ratio of the diffusing sphere. |
|
Observations & Results
Inverse Square Law
| Height ( metres ) | Illuminance lux ( lm/m2 ) | Product I = Ed2 ( Candelas ) |
| 1 | ||
| 1.5 | ||
| 2 | ||
| 2.5 | ||
| 3 |
Cosine Law
| Height above floor ( metres ) | Distance along floor ( metres ) | Distances from source to surface | Illuminance ( measured ) | Illuminance ( theoretical ) |
| 1 | 2 | |||
| 2 | 1 | |||
| 2 | 2 |
| Luminance of sphere (cd/m2) | Luminous intensity (candelas ) |
|
|
Explain the apparent discrepancy between these results and the Inverse Square Law.