Question

The illuminance of a small area changes from 900 lumen $m^{-}1$ 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 he original position .

Answer 1

$\text{Let, l=Luminous intensit of source}$

$E_A=900lumen/m^2$

$E_B=400lemen/m^2$

$Now,E_A=l\frac{cos\theta }{x^2}and$

$E_B=\frac{lcos\theta }{(x+10{)}^2}$

$S0,l=\frac{E_A{x}^2}{cos\theta }=\frac{E_A(x+10{)}^2}{cos\theta }$

$\Rightarrow 900x^2=400(x+10{)}^2$

$\Rightarrow \frac{x}{x+100}=\frac{2}{3}$

$\Rightarrow 3x=2x+20$

$orx=20cm$

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