Lambert's cosine law I am learning how to physically render images in computer graphics. I just saw that the area that gets light is given by the Lambert's cosine law.
In my head it makes perfect sense the relation but once I see the drawing I just cannot see the relation.
Can someone help me with a draw where I can see where does it come from or any suggestion on how to see it on a picture?
EDIT
After some thinking, I get to the following image according to the answer. Can someone confirm if this is ok?

 A: To model a diffuse surface, imagine a house that is on fire inside (!) so that everything inside is emitting light equally in all directions. You can also imagine a very hot oven or kiln in which the interior walls are aglow. Now, if you  look through the door of the house, the flux of light entering your eye is obviously proportional to the area of the door. In other words, proportional to the cross-sectional area of the column of light passing through the door on its way towards you.
If you view the door from an angle, then the effective area has been reduced by a factor of $\cos\theta$ where $\theta$ is the incident angle. The door you see has gotten narrower by a factor of $\cos\theta$, and the column of light similarly. To see this, draw a right triangle where the hypotenuse is the door, and one side lies parallel to the line between you and the door, while one side is perpendicular to that line. The angle between the hypotenuse and the second side is complimentary to the angle between the normal of the door and the line connecting you and the door. Hence the third side has length $hypotenuse \times \cos\theta$,
You can see the geometry of the situation in this image: http://www.idav.ucdavis.edu/education/GraphicsNotes/Shading/img86.gif
Now the door was letting out light in all directions equally, so if we instead imagine the door emitting light in all directions equally (*), then this is the same as a diffuse surface.
(*) This equivalence, I believe, depends on the inverse-square fall-off of intensity.
A: The geometry of the situation is often given backwards, this confused me too for a while. It is not the light intensity that remains fixed, but the surface area (even though in one instance they are equal).
This may not be as helpful a description from physics, but I found it helpful in a graphics setting.
We are interested in calculating the amount of light that hits a given area. Assume the light hits the surface flat on (the normal is 180$^\circ$ to the light). Then the light hitting the surface is equal to the intensity of the light. Call this $i_d$ (the diffuse component of the illumination).
Now shift the area to the right. The surface area is still the same, $i_d$. But now we can see that the 'width' of the beam of light hitting the surface is smaller. In fact it is $i_d\cos(\theta)$.

Realise this is an old question but hopefully that explanation helps someone. I've seen many examples where they fix the light width and calculate the new surface area, but doing the maths leads to $\frac{i_d}{\cos(\theta)}$.
A: There is no true photo of light scattered from a surface that obeys Lambert's cosine law.
The Scattered light is considered in the literature as a diffusive light, light that passed a number of scattering events before it left the scattering material. Diffusely scattered light must obey Lambert's Cosine scattering law. In the case of unidirectional light scattered backward from a surface of a sphere, the meaning is maximum scattering intensity in the middle of the sphere, and a decline to zero toward the periphery by the cosine law.
The full moon looks uniform and people continue to assume that the light is diffusely scattered from it.
More than that. The nearly uniform sphere image is common to all the planets and their moons, including the earth as observed from space and the moon. Out of thousands upon thousands of true photos, there is no single true photo that obeys Lambert's Cosine law. The only photos that do obey the law are rendered photos, photos that are at least partly simulated.
Contrary to all that, if the scattering is assumed to be mainly a single event, then all the scattering dipoles are directly stimulated by the light radiation on the illuminated scattering material. Then scattering by them must be coherent, and then the full moon and all the other illuminated bodies, with similar illumination geometry, must be uniform, at least approximately. The full moon tells us that single event scattering is dominant. Maybe with small corrections of multiple scattering.
Why is the single event dominant? It seems that the effect is geometrical and statistical. If we consider one event scattering, two event scattering, multiple event scattering, then the event probability will decline with an increasing number of scatterings. The single event has a probability of at least 50% and it is the strongest event.
Nearly all the background that surrounds us is a singly scattered light. A true diffusely scattered light is rather rare.
In summary, the mean backscattering from the full moon is directed back to the sun because the scattering dipoles on the moon oscillate in a plane perpendicular to the coming sunlight.
