TE Enriched Sample (E)

26 Lighting 1 Michelle chooses a CFL for her bedroom of dimensions 4 m × 4 m × 2.7 m. The energy label of the lamp is shown on the right. 4 m 4 m 2.7 m A B more efficient Ref/Yr L080123/08 Compact Fluorescent Lamp less efficient : EMSD 60 Lumen/W ( ) 1 2 3 4 5 Grade (a) The rating of the CFL is 20 W. What is its luminous flux? (b) Treat the CFL as a point light source O . Two small surfaces A and B are on the floor. A is directly below the lamp and B is next to the wall. Find the illuminance on them. (c) Aworker measures the illuminance in (b) but finds that the actual values are greater. Briefly explain why. Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) Luminous flux U = 60 × 20 = 1200 lm . (b) Light is incident perpendicularly on A . The illuminance on A is ( . ) . E r 4 4 2 7 1200 13 10 A 2 2 r r U = = = . 13.1 lx Consider i OAB . We have . . . cos 2 2 7 2 7 0 8036 2 2 i = + = . The illuminance on B is . ( . ) cos cos E d E 4 13 10 0 8036 B A 2 3 3 3 # r i i U = = = . 6.80 lx A B 2.7 m 2 m O θ Brightness on a surface Example 1.3 Alternative Consider i OAB . OB 2 = 2 2 + 2.7 2 = 11.29 m 2 . ( . ) ( . ) cos E r 4 4 11 29 1200 0 8036 B 2 r i r U = = . 6.80 lx (c) The diffuse reflection of light from the wall and the ceiling is neglected in the above calculations. What-if . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . C is a small surface next to B , but it is on the wall . Is the illuminance on C the same as that on B ? Ans: No. The value of θ is larger for C and hence the value of cos θ is smaller. Teaching notes Remind Ss that reflection of light is important in reality and neglecting reflection is usually not a good approximation in many cases. 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.