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the amount of illumination of a surface is proportional to the intensity of the light source,

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From the given information we can derive an equation for illumination 

image  -----------(1)

Where I is the amount of illumination

d is the distance from light source 

k is constant

Now we have to simplify the diagram

Here L is the position of light and c is corner of room

Then d is distance from light source to corner of room

        a is angle of incidence 

From the figure 


Put the values of d and sin a in equation (1)


To find out the height of light as much as possible , we make it's first derivative to zero


h = 9.192 ft

So height of light to be placed to cover maximum light as possible is h = 9.192 ft

answered Oct 10, 2014 by friend Mentor

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