Question

the amount of illumination of a surface is proportional to the intensity of the light source, inversely proportional to the square of the distance from the light source, and proportional to sin(a) , where a is the angle at which the light strikes the surface. A rectangular room measures 10ft by 24 ft , with a 10foot ceiling. determine the height at which the light should be placed to allow the corners of the floor to receive as much light as possible

Answer 1

From the given information we can derive an equation for illumination 

  -----------(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