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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Is this only because the greater the angle, the greater the surface area that the beam interacts with? Or are there other factors?