Calculating Torch Brightness Using Angle & Distance

[jackbrookes]

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?

 

[LCKurtz]

You might find the formulas near the bottom of the page at

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

useful.