TE Enriched Sample (E)

27 Measuring illumination 1.3 Jimmy is choosing a lamp for his dining room. The lamp will be 1.6 m above the centre of a circular table of radius 1.2 m. Moreover, he wants every part of the table to have an illuminance of over 20 lx. 1.6 m 1.2 m (a) Which part of the table is least illuminated? According to Jimmy’s criteria, what is the minimum luminous flux that the light source should produce? State any assumptions made in your calculations. (b) If the efficacy of the lamp is 64 lm W - 1 , find the total electricity cost of using the lamp for one year. Assume the lamp is used 6 hours a day and the electricity cost is $0.9 per kW h. (c) Suggest a method to reduce the electricity cost while providing enough illuminance on the table. Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) The edge of the table is least illuminated as it is farthest from the lamp and has the largest incident angle. At the edge, . . . . cos 1 2 1 6 1 6 0 8 2 2 i = + = Neglect any reflection of light from the ceiling and the walls. If the illuminance on the edge of the table is E = 20 lx, . ( ) ( . ) lm cos cos cos E E d Ed 4 4 0 8 4 20 1 6 1257 1260 0 0 2 3 3 0 2 3 2 ` . i r i i r r U U = = = = = (b) The rated power of the lamp is 64 1257 = 19.63 W. The annual total energy consumption is 19.63 × 6 × 365 = 43 000 W h = 43.00 kW h The electricity cost is 43.00 × 0.9 . $38.7 . Providing adequate brightness Example 1.4 Sample © United Prime Educational Publishing (HK) Limited, Pearson Education Asia Limited 2023 All rights reserved; no part of this publication may be reproduced, photocopied, recorded or otherwise, without the prior written permission of the Publishers.