Aim:

To determine the relationship, if any, between light intensity and distance from a lamp. It is obvious that light intensity drops as you move further away from the light source.  Theoretically, with all other factors being equal, the inverse square rule should dominate the change in intensity.

The inverse square rule states that if the intensity at point X from a single point light source is A, the intensity at X+Y will be A/Y^2.

Method:

A lamp was positioned on a bench top such that it was pointing in a direction parallel to the top of the bench.  Light readings were taken at various distances from the light source and recorded.

The lamp used was a 150W Metal Halide light, fitted with a 150W 10000K double-ended lamp (BLV 221301).  The lamp was around 12 months old.

A second test was performed using normal output fluorescent lighting.  A new 30W Sylvania Aquastar was fitted to simple light fitting.

The meter used was a Basic Quantum Meter with Electric Light Calibration made by Apogee Instruments.  The meter measures Photosynthetic Photon Flux in µE m^-2s^-1 (microeinsteins per square metre per second). A microeinstein is equivalent to a micromole of photons. The meter responds to light in the range 400-650nm.  It underestimates light in the range 400-500nm (blue light) and overestimates light in the range 550-650nm (yellow and orange light).  It is rated at an accuracy of +/-3%.

The bench top was covered with a grey blanket to reduce reflection.

Measurements for the Metal Halide lamp were taken from the outside of the UV filter on the fixture.  From the outside of the UV filter to the outside of the outer lamp envelope is 1cm. The inner lamp envelope is a further 0.4cm from the outer envelope.  The inner and outer envelopes are approximately 1.5cm and 2.3cm in diameter, respectively.

The lamp was fired at least 5 minutes before the tests begun, and the first reading was taken after the meter read a "constant" value for at least one minute. At close distances to the light source, the light output is very high and the meter records variations of up to 2 µE m^-2 s^-1.

Measurements for the Fluorescent lamp were taken from the centre of the tube and 20cm from the centre.

Results:

Table 1: Meter readings from the MH lamp at different distances from the UV Filter

Distance from UV filter (cm)	Reading 1 (µE m-2 s-1)	Reading 2 (µE m-2 s-1)	Reading 3 (µE m-2 s-1)	Average PAR (µE m-2 s-1)
10	1433	1410	1411	1418
15	801	802	799	801
20	499	497	501	499
25	249	349	338	312
30	249	250	249	249
35	190	190	190	190
40	149	149	148	149
50	100	99	100	100
60	72	71	72	72
70	59	53	53	55
80	42	41	41	41
90	33	33	32	33
100	28	27	28	28
110	22	22	22	22
120	19	19	19	19

Table 2: Light intensities for the MH lamp at the corrected distances from the light source. As the measurements were taken from the outside of the UV filter, 2.3cm was added to give the distance from the centre of the lamp.

Distance from light (cm)	Average (µE m-2 s-1)
12.15	1418
17.15	801
22.15	499
27.15	312
32.15	249
37.15	190
42.15	149
52.15	100
62.15	72
72.15	55
82.15	41
92.15	33
102.15	28
112.15	22
122.15	19

Table 3: Meter readings for the centre of the fluorescent tube.  Distances are measured from the tube.

Distance from light (cm)	Reading 1 (µE m-2 s-1)	Reading 2 (µE m-2 s-1)	Reading 3 (µE m-2 s-1)	Average (µE m-2 s-1)
10	108	102	101	104
15	78	79	79	79
20	57	58	58	58
25	49	49	49	49
30	37	37	37	37
35	31	31	30	31
40	28	28	29	28
50	19	19	19	19
60	19	19	19	19
70	17	17	17	17
80	9	9	9	9
90	7	7	7	7
100	8	8	8	8
110	9	9	9	9
120	9	9	9	9

Table 4: Meter readings for 20cm from the centre of the fluorescent tube.

Distance from light (cm)	Reading 1 (µE m-2 s-1)	Reading 2 (µE m-2 s-1)	Reading 3 (µE m-2 s-1)	Average (µE m-2 s-1)
10	108	113	111	111
15	77	78	78	78
20	58	58	59	58
25	43	43	47	44
30	39	39	33	37
35	28	28	27	28
40	23	23	22	23
50	17	17	18	17
60	13	13	13	13
70	10	10	10	10
80	8	8	8	8
90	7	8	7	7
100	8	9	8	8
110	9	9	9	9
120	9	9	9	9

Interpretation: