Doubt about distribution

[antoniogamiz]

In the first book, RayTracingInOneWeekend, section 8.5. True Lambertian Reflection, it says that

the distribution scales by cos^3(phi)

Anyone knows where's that proven? Could you please send me a reference to some book or similar where that is explained? I mean the mathematics behind that fact.

[rjkilpatrick]

This appears to be a duplicate of #530 , I will try and answer this later this week.

[trevordblack]

See comment #530 (comment)

I very much doubt that we can explain (succinctly) that the distribution is cos^3(phi).
I can see if there is (at most) 2 sentences that can lend an intuition.
It's already a pretty over-stuffed chapter and in need of some editing. See #696 #530 #617

Ultimately, I think the best thing would just be a citation, which is blocked by #299 #407

In the meantime, the comment above has what you're looking for.