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The illuminance of a small area changes ...

The illuminance of a small area changes from 900 lumen m^-2 to 400 lumen m^-2 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 the original position.

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The correct Answer is:
B, C
Let, l=Luminous intensity of source
E_A=900 lumne/m^2`
`E_B=400 lumen/m^2`
Now,` E_a=(costheta)/x^2` and
`E_B=(lcostheta)/((x+10)^2)`
so, `l=(E_Ax^2)/(costheta)=(E_A(x+10)^2)/(costheta)`
`rarr 900x^2=400(x+10)^2`
`rarr x/(x+10)=2/3`
`rarr x=2x+20`
`or x=20 cm`
So the distance between the source and the origiN/Al position is 20 cm.
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