Recent content by enslay

What's inappropriate about starting with a point source emitting "photons" in uniform random 3D directions and transforming that distribution into a distribution of "photons" hitting a parameterized surface? It's not like I chose to have an infinite plane before hand. The infinite support...

Sweet! And this is certainly easier to derive than using conditional probabilities. It's neat that I got the same answer though! To deal with the vanishing intensity in ##R \to \infty##, I essentially considered the ratio of the intensities at a location ##(y,z)## for the ##x=2R## and ##x=R##...

I guess in general for a vertical plane at position ##x=R##, you have a surface normal vector in the direction of ##[1,0,0]^T## with the distance of the point source to the plane being ##|R - x_0|##. So if I understand the definition of the angle of incidence ##\theta## correctly (that being the...

OK, I just talked with the a physicist about the angle of incidence and this may be where that extra 1/r comes from. I'll have to play around with the math on the angle incidence and see what I get. I didn't mean for this to be a heated discussion. I never disputed the inverse square law. I...

Yeah OK, maybe the topic title isn't the greatest. That's a fair point. I'm not quite sure what you're suggesting with 1/R. Is it that in a 2D world, there is an inverse law and it is approximately true in your density for small y?

This is not helpful and borderline insulting. Where is the crackpottery? I am always open to be corrected. You never correct me though. So it inevitably leads to more complicated expression right? Alright... so how can I set this right with physicists who try to use the inverse square law to...

The story is that I work with physicists who try to derive the density using the inverse square law. The inverse square law is verified and true, right? Seems reasonable. They insist that they can predict the intensity on the detector surface (e.g. a plane, a cylinder) with the inverse square...

I was thinking of deriving everything with solid angles for you to make you happy. It should give the same exact result. And wow, that article is not very nice to read. It's even more complicated than deriving the sphere density. I think I'll stick with using conditional probabilities (where I...

I don't think I contradicted the inverse square law, did I? I know it's been experimentally verified, but it's also (usually) trivial to transform a uniform random direction density into a density describing how "photons" hit a surface. So the math is straightforward for that too. That's the...

TL;DR Is it correct to say that inverse square law is only exactly true for sphere surfaces whenever the point source is centered in the sphere? For other cases, it seems to be only approximate (could be a bad approximation for "small" R) and only asymptotically true. Is this all a correct...

OK, I think it works out! I just tried the planar detector which is nice and easy. And I think I messed up with the sphere detector over the weekend. I will do it again... So let's fix the histogram bin size to ##\Delta y,\ \Delta z##. Then for N photons (italics because they are purely...

Oh my, I didn't get any e-mail notifications about these responses. Apologies for the delayed response. OK, but we're not in a 2D world. The 2D detector densities always seem to have the expected 1/r^2. It's only when you go into 3D detector densities that you get these odd 1/r^3. Worse yet, it...

Perhaps I misspoke. I only call the purely mathematical objects "photons". There is no explicit physics in the derivation. I guess you could say I'm assuming discrete objects traveling in a uniform random 3D direction from ##(x_0,y_0,z_0)## which I guess I erroneously call "photons". Sorry...

Done. This is the first forum I have ever seen that supports LaTeX. I didn't even know it was an option. Yep, it's definitely a gotcha! And I did make that mistake in the past. I do properly account for this. I love the below site and it even visually shows you the difference between the...

Hello, This is my first post. For background, I have asked Ask The Physicist who has posted our correspondences and answers here: https://www.askthephysicist.com/ask_phys_q&a.html Search "My question is with regard to an apparent mathematical disagreement" or something like that to find the...