Black body, angle of incidence

[Incand]

I'm trying to understand the solution to an exercise.
The solution claims that that the absorbed power of a black body from sunlight with an angle of incidence of ##30^\circ## is
##P=P_0\cos(30^\circ)##
The reasoning here being to take the component orthogonal to the surface.

However what puzzles me is that wikipedia article on black body https://en.wikipedia.org/wiki/Black_body
says that "A black body is an idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence."

Shouldn't this mean that all the power should be absorbed regardless of the angle of incidence?

 

[Ibix]

Imagine holding a sheet of paper flat on a table, absorbing some amount of power from a lightbulb directly overhead. What happens to the total power falling on the sheet if you tip it away from horizontal?

 

[Incand]

I actually tried to do that experiment now! It's hard to tell with only the eyes and with other light sources around but the paper does indeed seem to get darker.

So if we consider a small portion of the light what happens when we tilt the paper is that the same amount of light is distributed over a larger surface. So if the light enter with angle ##\theta## the area of our small portion of light is distributed over ##A=A_0/ \cos \theta## and then the power per area is ##P = P_0/A = P_0 \cos \theta / A_0##. Thanks!

 

[Ibix]

Experimental test - nice.

On a large scale this is why winter is colder than summer. In northern hemisphere winter the north pole points away from the sun, so the sun is lower in the sky at noon than in summer (when the north pole is tilted towards the sun). The more oblique angle means less solar radiation per square meter of ground, which makes it colder.

The special thing about black bodies is that they absorb all the radiation falling on them at any angle. The cosine behaviour comes from the projected area as you've seen. Non-black bodies reflect some fraction of the radiation, and the fraction may vary at different angles, so their behaviour may vary from the cosine.