Assignment problem..?

[1123581321]

Hi, i doing an assignment in an algebra and differential calculus unit and it asks the following:

 

The brightness, I, of a light beam that illuminates some surface is expressed by: I = (k*sinx)/(r^2), where k is a constant for the given source, r is the distance between the source and the illuminated point and x is the angle between the light ray and surface. at what height should you suspend a lamp over a round table of radius, a, so that the edge of the table is maximally bright. ?

 

and in the old soln, it has: h = a/(square root of 2), but i dont understand how they get there...

 

If anyone could give me something to go with that would be great, because the way its worked out doesnt make sense to me.

thanks.

[studiot]

Well you haven't shown any working at all, even a diagram would have been a start.

A diagram would at least confirm what you have said in words.

 

Here is a hint.

 

Taking your words literally

 

If h is the height then do you have an equation connecting h and I?

 

Draw a triangle showing r, x, h

 

You should now be able to substitute into the equation you posted for sinx and r to obtain an equation between I and h.

 

Now over to you.