Incident light angle brightness

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when light hits a surface at an angle. it is darker if it hits it at higher angle(facing away) than at a lower angle(facing towards). 1


Is there a formula for the brightness.The relationship of angle to brightness does not look linear.


http://www.vam.ac.uk/vastatic/microsites/1384_leonardo/animated_illustrations/view/?movie=light" 1
 
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The brightness would go like cos of the angle.
 
Is this only because the greater the angle, the greater the surface area that the beam interacts with? Or are there other factors?
 
It is just that Intensity = Power/area
 
There is also an inverse-square dependence, which is negligible if (for example) a point-like source is very far from the surface.