TE Enriched Sample (E)

25 Measuring illumination 1.3 Aworker measures the illuminance of a surface at a distance of 1.5 m from a small lamp. The reading is 64 lx. (a) What is the luminous flux produced by the lamp? (b) How does the reading change if the distance is 3 times the original? The orientation of the lux meter remains unchanged. Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . (a) By E r 4 2 r U = , the luminous flux U is (64) × 4 r (1.5) 2 . 1810 lm . (b) Since E r 1 2 ? , the reading (illuminance) is reduced to 9 1 when the distance is 3 times the original. Luminous flux Example 1.2 Point light source and oblique incidence If the light source is small and the surface is not perpendicular to the incident light, we may combine the inverse-square law and Lambert’s cosine law to find the illuminance on a small surface. Consider a point light source of luminous flux U at a height d above a floor (Fig. 1.26). At a distance r from the source, the illuminance on a surface normal to the incident light is E r 4 0 2 r U = Suppose a small surface X is ȱȱ and at a distance r from the source. The luminous flux falling on X is cos cos E E r 4 0 2 $ i r i U = = ; ; Ö spreading Ö at an angle where cos θ = d / r . Sometimes it is more convenient to express the illuminance in terms of d (= r cos θ ). The above equation becomes cos E d d 4 4 2 2 3 r i r U U = $ cos i = $ cos i J L K N P OO d r X θ θ point light source Fig. 1.26 Lambert’s cosine law for a point light source The angle of incidence θ is measured from the normal of the illuminated surface. Here, cos θ is given by d / r . Teaching notes Remind Ss that, in cases with mirror reflection, treat the mirror image of the lamp as the light source (see DSE 2022 Q3.2). A further question can be added to Ex. Q9 on p. 29 as an exercise: changing the wall at the back to a mirror. Teaching notes Remind Ss that θ is the angle of incidence to the illuminated surface. To pick the correct angle, identify the illuminated surface (and its normal) and the angle by their own. Never trust any label θ given in the question. (See DSE 2016 Q3.2, 2019 Q3.1) θ illuminated signage light source θ ( MC: DSE 2012 Q3.2, 2015 Q3.1, 2016 Q3.2, 2017 Q3.1, 2019 Q3.1) 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.