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Appropriate Use of the Inverse Square Law
Partridge, C (1978). 'Community physiotherapy', Developmental Medicine and Child Neurology, 20, 8 0 2 - 804. Pennefather, M E and Tanner, E R (1968). 'Physiotherapy in general practice', The Practitioner, 201, 9 3 3 - 9 3 7 . Petty, T L. Bransqomb. B V. Farrington. J R L, Kettel, L J and Lindesmith. L A (1974). 'Community resources for rehabilitation of patients w i t h chronic obstructive pulmonary diseases or cor pulmonale', Circulation, 69. A1 A20. Rankin, N, Meyer, R and Bauer, D (19771. 'Shared physiotherapy in a rural setting', Dimensions in Health Service, 54, 4 3 - 4 5 . Richter, R W, Bengen, B, Bruun, B, Kilcoyne, M. Alsup, P A, Shafer, S Q, Brown, R H, Brust, J C M and Dorset, V E (1974). 'Example of a community model for comprehensive stroke services: The Harlem regional stroke program', Stroke, 5, 135-143. Rossman, I, Clarke, M and Rudnick, B (1962). 'Total rehabilitation in home care setting', New York State Journal of Medicine, 62, 1215-1219. Royal College of Physicians (1986). The Young Disabled Adult and The Use of Residential Homes and Hospital Units for the Age
Group 16-64. Strawczynski, H. Stachewitsch. A, Morgenstren, G and Shaw, M E (19731. 'Delivery of home care to haemophilic children: Home care versus hospitalisation', Paediatrics, 51, 986-991. Tunbridge, R (1972). Rehabilitation, Report of a sub-committee of the Standing Medical Advisory Committee, HMSO. United States Department of Health, Education and Welfare: Public Health Service (1964). Co-ordinated Home Care Programmes. Waters, W H R, Udy, S C and Lunn, J E (1975). 'Organising a physiotherapy service in general practice', Journal of the Royal College of General Practitioners, 25, 5 7 6 - 584. Wilson, R E (1976). 'The role of the physiotherapist in the Community', Australian Family Physician, 5 , 6 8 4 - 693. Wolcott, L E. Wheeler, P C, Ballard, P, Crumb, C K, Miles, G and Mueller. A (19661. 'Home-care versus institutional rehabilitation of stroke: A comparative study,' Missouri Medrcine, 63, 722 724. Yorke, R A (1974). 'Domiciliary physiotherapy service' (letter), The Lancet, 11, 214.
Appropriate Use of the Inverse Square Law 50
\;
Intensity = mean of three lamps with standard deviations
-:1
I
The Inverse Square Law, formulated by Sir Isaac Newton, states that 'the intensity of radiation emitted by a point source is inversely proportional to the square of the distance from that source'. The physiotherapist uses this relationship frequently when calculating the dose of ultra-violet light that the patient will receive from a lamp.
THEORETICALLY any radiant emitter ceases to act as a point source when backed by a reflecting surface. Thus, one might conclude that the inverse square law should not be used t o calculate the intensity of radiation generated by most therapeutic lamps, which invariably incorporate a reflector, in the clinical situation. This hypothesis was tested by measuring the intensity of the emission from three Hanovia Alpine Sun 10 ultra-violet lamps fitted with 504/4 discharge tubes, and used previously for 10, 5 0 and 70 hours. Each lamp was warmed up, and the output allowed to stabilise for 15 minutes before the intensity of emission was measured in a darkened room. The measurements were made using a voltmeter to indicate the output of a thermopile (Applied Photophysics Inc) that acted almost as a true black body for radiations between far ultra-violet and infra-red. The output of each lamp was determined at five distances from the discharge tube ( 2 9 cm; 44 cm; 8 6 cm; 116 cm; 158 cm), the thermopile being accurately centred under the lamp using a plumb-line, and supported on a non-reflective surface. The results are summarised in the figure. and indicate, surprisingly, that the inverse square law does indeed predict accurately the intensity of radiation at distances between 1.58 m (the maximum measured), and 0.5 m from the source. However, the intensity at distances less than 0.5 m was lower than that predicted theoretically. The discharge tubes of these lamps appear t o be backed by such a poorly-reflecting surface (anodised aluminium), and to be so compact (4c m wide) that they act as a point
8
-
40
Intensity = calculated using inverse square law --
I
_--
^y
2E 30 E
I
>. .-c In
I
I
\i:
X'
c 20
(L1
-c *-'
10
\
\ r
- X
C
L
50 100 150 Distance from discharge tube (cm)
200
Effect of distance upon intensity of radiation emitted by Hanovia UV lamps
source when removed to a distance greater than 0.5 m. The clinical implications of these results are clear. The inverse square law does not theoretically apply to lamps with reflectors. The law may, however, be used as a rule of thumb t o calculate the variation in intensity of output due to distance, provided that the patient is more than 0 .5 m from the source. At distances less than 0.5 m the patient will receive a slightly smaller dose of radiation than that predicted by this law, and will also experience the undesirable heating that results from close proximity to the tube. ACKNOWLEDGMENT I acknowledge w i l h thanks the assistance of M r J Feather,
Department of Medical Physics, General Infirmary at Leeds, in making these measurements
Physiotherapy, Jariuary 1988, vol 74, no I
Group 16-64. Strawczynski, H. Stachewitsch. A, Morgenstren, G and Shaw, M E (19731. 'Delivery of home care to haemophilic children: Home care versus hospitalisation', Paediatrics, 51, 986-991. Tunbridge, R (1972). Rehabilitation, Report of a sub-committee of the Standing Medical Advisory Committee, HMSO. United States Department of Health, Education and Welfare: Public Health Service (1964). Co-ordinated Home Care Programmes. Waters, W H R, Udy, S C and Lunn, J E (1975). 'Organising a physiotherapy service in general practice', Journal of the Royal College of General Practitioners, 25, 5 7 6 - 584. Wilson, R E (1976). 'The role of the physiotherapist in the Community', Australian Family Physician, 5 , 6 8 4 - 693. Wolcott, L E. Wheeler, P C, Ballard, P, Crumb, C K, Miles, G and Mueller. A (19661. 'Home-care versus institutional rehabilitation of stroke: A comparative study,' Missouri Medrcine, 63, 722 724. Yorke, R A (1974). 'Domiciliary physiotherapy service' (letter), The Lancet, 11, 214.
Appropriate Use of the Inverse Square Law 50
\;
Intensity = mean of three lamps with standard deviations
-:1
I
The Inverse Square Law, formulated by Sir Isaac Newton, states that 'the intensity of radiation emitted by a point source is inversely proportional to the square of the distance from that source'. The physiotherapist uses this relationship frequently when calculating the dose of ultra-violet light that the patient will receive from a lamp.
THEORETICALLY any radiant emitter ceases to act as a point source when backed by a reflecting surface. Thus, one might conclude that the inverse square law should not be used t o calculate the intensity of radiation generated by most therapeutic lamps, which invariably incorporate a reflector, in the clinical situation. This hypothesis was tested by measuring the intensity of the emission from three Hanovia Alpine Sun 10 ultra-violet lamps fitted with 504/4 discharge tubes, and used previously for 10, 5 0 and 70 hours. Each lamp was warmed up, and the output allowed to stabilise for 15 minutes before the intensity of emission was measured in a darkened room. The measurements were made using a voltmeter to indicate the output of a thermopile (Applied Photophysics Inc) that acted almost as a true black body for radiations between far ultra-violet and infra-red. The output of each lamp was determined at five distances from the discharge tube ( 2 9 cm; 44 cm; 8 6 cm; 116 cm; 158 cm), the thermopile being accurately centred under the lamp using a plumb-line, and supported on a non-reflective surface. The results are summarised in the figure. and indicate, surprisingly, that the inverse square law does indeed predict accurately the intensity of radiation at distances between 1.58 m (the maximum measured), and 0.5 m from the source. However, the intensity at distances less than 0.5 m was lower than that predicted theoretically. The discharge tubes of these lamps appear t o be backed by such a poorly-reflecting surface (anodised aluminium), and to be so compact (4c m wide) that they act as a point
8
-
40
Intensity = calculated using inverse square law --
I
_--
^y
2E 30 E
I
>. .-c In
I
I
\i:
X'
c 20
(L1
-c *-'
10
\
\ r
- X
C
L
50 100 150 Distance from discharge tube (cm)
200
Effect of distance upon intensity of radiation emitted by Hanovia UV lamps
source when removed to a distance greater than 0.5 m. The clinical implications of these results are clear. The inverse square law does not theoretically apply to lamps with reflectors. The law may, however, be used as a rule of thumb t o calculate the variation in intensity of output due to distance, provided that the patient is more than 0 .5 m from the source. At distances less than 0.5 m the patient will receive a slightly smaller dose of radiation than that predicted by this law, and will also experience the undesirable heating that results from close proximity to the tube. ACKNOWLEDGMENT I acknowledge w i l h thanks the assistance of M r J Feather,
Department of Medical Physics, General Infirmary at Leeds, in making these measurements
Physiotherapy, Jariuary 1988, vol 74, no I