Question

can anybody explain me why in lambert's cosine law the area changes to a cos thita

Answer 1

The angles of the slices of the scatter circle are all constant. It is the areas of the slices that are different. The areas are dependent on the cosine of the angle, theta, which is the angle away from the perpendicular at which the photon receptor, or measure, or eye sits. These areas are proportional to the number of photons scattered in that slice of circle: the larger the slice area, the greater the number of photons.

So qualitatively, we would expect more light to be reflected back near to the perpendicular than we would expect to be scattered at an angle approaching 90 degrees. ie It is more likely that a photon will be reflected straight back near to the perpendicular than to be turned through something approaching 90 degrees which will mean turning a right angle and shooting along the plane of the surface.

http://www.flickr.com/photos/sgulasch/3279367236/

Answer 2

anybody have mathematical proof

Answer 3

Wikipedia, my friend, has almost everything...
http://en.wikipedia.org/wiki/Lambert's_cosine_law