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Assignment problem..?

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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.


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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.

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