Calculating Torch Brightness Using Angle & Distance

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The discussion centers on calculating the brightness of light from a torch based on the angle and distance from a wall. The user proposes a formula for brightness, B, which is inversely related to the square of the distance multiplied by the tangent of the angle. They express uncertainty about the accuracy of their formula and seek confirmation or correction. The relationship between the angle of light, distance, and brightness is crucial for understanding how light spreads. The conversation highlights the need for clarity on the properties of light and how they affect brightness calculations.
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Hi I'm new here and I'd like some help with something that's been niggling me for the past few days. I've yet to study Maths or Physics at A Level (UK), so this should be easy for some of you.

If I were to shine a torch that shone a circular, even spreading of light, what would be the relationship between the angle of the light coming from the torch, the distance from a wall, and the brightness on the wall?

Here's what I've got: (this is assuming there isn't a property of light that I don't know about)

B=Brightness
D=Distance from wall
X=Angle, As in Shining at 90 degrees would actually shine 90 up and 90 down

B=1/(pi*(D*TanX)^2)

D*TanX=Radius, so pi*r*r=a

http://www.wolframalpha.com/input/?i=Plot3D[Cot[X

However it just doesn't seem right. Is this right or wrong?
 
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You might find the formulas near the bottom of the page at

http://www.dcmsistemes.com/medidasi.html

useful.
 

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