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Question

The illuminance of a small area changes from 900 lumen m1 to 400 lumen m2 when it is shifted along its normal by 10 cm. Assuming that it is illuminated by a point source placed on the normal, find the distance between the source and the area in he original position .

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Solution

Let, l=Luminous intensit of source

EA=900 lumen/m2

EB=400 lemen/m2

Now,EA=lcos θx2 and

EB=l cos θ(x+10)2

S0,l=EAx2cos θ=EA(x+10)2cos θ

900x2=400(x+10)2

xx+100=23

3x=2x+20

or x=20 cm

So, The distane between the source and the original position is 20 cm.


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